TRIGONOMETRICAL IDENTITIES - PART - 29

57. cos A /(1 + sin A) = sec A – tan A

58. cos A /(1 – sin A) = (sin A – cos A +1) / (sin A + cos A –  1)

TRIGONOMETRICAL IDENTITIES - PART - 28

55. 2 sin² A + cos⁴ A – sin⁴ A = 1

56. (tan A + cot A)(cosec A – sin A)(sec A – cos A) =1 

TRIGONOMETRICAL IDENTITIES - PART - 27

53.  sec⁴ A (1 – sin² A) – 2 tan² A = 1

54. cosec⁴ A (1 – cos² A) – 2 cot² A = 1

TRIGONOMETRICAL IDENTITIES - PART - 26

51. (1 + cot A – cosec A) (1+ tan A + sec A) = 2

52. (1 + tan A –  sec A) (1+ cot A – cosec A) = 2

TRIGONOMETRICAL IDENTITIES - PART - 25

49. [cosec A /cosec A – 1)]+[cosec A/cosec A +1)] 2 sec² A

50. [sec A /sec A – 1)] + [sec A /sec A +1)] = 2 cosec² A

TRIGONOMETRICAL IDENTITIES - PART - 24

47. 1 – [( sin² A) / (1 + cos A)] = cos A

48. 1 – [( cos² A) / (1 + sin A)] = sin A 

TRIGONOMETRICAL IDENTITIES - PART - 23

45. (cos A / (1 + sin A) + tan A = sec A 

46. (sin A / (1 – cos A) – cot A = cosec A

TRIGONOMETRICAL IDENTITIES - PART - 22

43. (1 / (sin A – cos A) / (1 /(sin A + cos A) =  2cos A / (2sin² – 1)

44. (1 / (cos A + sin A) / (1 / (cos A – sin A)  = 2cos A / (2cos² – 1)

TRIGONOMETRICAL IDENTITIES - PART - 21

41. (sin A) / (1 + cos A) =  (cosec A + cot A)

42. (cos A) / (1 - sin A) =  (sec A + tan A)

TRIGONOMETRICAL IDENTITIES - PART - 20

39. (1 - sin A) / (1 + sin A) =  (sec A – tan A)²

40. (1 - cos A) / (1 + cos A) = (cot A – cosec A)²

TRIGONOMETRICAL IDENTITIES - PART - 19

37. (1 - sin A) / (1 + sin A) =  cot² A / (cosec A + 1)²

38. (1 + cos A) / (1 - cos A) = tan² A / (sec A - 1)²

TRIGONOMETRICAL IDENTITIES - PART - 18

37. (1 - sin A) / (1 + sin A) =  cot² A / (cosec A + 1)²

38. (1 + cos A) / (1 - cos A) = tan² A / (sec A - 1)²

TRIGONOMETRICAL IDENTITIES - PART - 17

33. sec² A .cosec² A = tan² A + cot² A + 2

34. (sin A + cosec A)² + (cos A + sec A)²= 7+ tan²A + cot² A

TRIGONOMETRICAL IDENTITIES - PART - 16

31. (sec A – tan A) / (sec A + tan A) = 1 – 2 sec A tan A + 2 tan² A

32. cosec A + cot A = 1 / (cosec A – cot A)

TRIGONOMETRICAL IDENTITIES - PART - 15

29. (cos A + sin A)² + (cos A – sin A)² = 2

30. (sec A – cos A) (sec A + cos A) = cot² A + cos²

TRIGONOMETRICAL IDENTITIES - PART - 14

27. (cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1

28. 1 / (sec A + tan A) = sec A – tan A

TRIGONOMETRICAL IDENTITIES - PART - 13

25. (cosec A + sin A) (cosec A – sin A) = cot² A +  cos² A

26. cot² A – cos² A = cos² A . cot² A

TRIGONOMETRICAL IDENTITIES - PART - 12

23. (1 + tan²A) (cot A) / cosec² A = tan A

24. tan² A – sin² A = tan² A . sin² A

TRIGONOMETRICAL IDENTITIES - PART - 11

21. cosec A (1 + cos A) (cosec A = cot A) = 1

22. sec² A + cosec² A = sec² A . cosec² A

TRIGONOMETRICAL IDENTITIES - PART - 10

19. (1 + tan² A) + (1 + 1/tan²) = 1 / (sin²A – cos²A)

20. [cos A /(1 –  tan A)] + [sin A / (1 – cot A)] = cos A + sin A

TRIGONOMETRICAL IDENTITIES - PART - 09

17. sec A (1 – sin A) (sec A + tan A) = 1

18. cosec⁴ A –  cosec² A = cot⁴ A + cot² A

DAILY TEN WORDS - HIGH-FREQUENCY WORDS IN ENGLISH - A - LIST - COMPILED BY ZENMURALI

681. awry (adj ) தவறி, இடக்குமுடக்காக, கோணலாக, உருத்திரிந்து

out of the proper form, direction or position, crookedly, wrong [adv – awry]

# The drama is to start at 2pm, but something went awry and it didn’t start until 3pm.

Ant. on course, ok

682. axiom (n) ஒத்துக்கொள்ளப்பட்ட கருத்து, வெளிப்படை உண்மை

accepted or established principle or self-evident truth [adj – axiomatic]

# Truth alone triumphs is an axiom.

Ant. contradiction, paradox, absurdity

683. aye (n) ஆம் என்னும் பதில்

an expression of assent, affirmative answer or vote

# The party’s stand is “no to sex education and aye to moral classes”.

Ant. nay, no, negative vote

684. azimuth (n) திசைக்கோணம்

the azimuth of a celestial body is the angle between the vertical plane containing it and the plane of the meridian [adj – azimuthal, adv – azimuthally]

# The azimuth angle is an important parameter in the design of solar towers.

685. azure (n) வானீல நிறமான

deep sky blue [adj – azure]

# The boats sailed under azure skies.

TRIGONOMETRICAL IDENTITIES - PART - 08

15. (sec A – tan A) ) /(cosec A + cot A) =  ((cosec A – cotA) ) / (sec A + tan A) 

16. (𝐭𝐚𝐧 𝐀 +𝐬𝐞𝐜 𝐀) ) /((𝐭𝐚𝐧 𝐀 − 𝒔𝒆𝒄 𝐀+𝟏)  ) =  ((𝟏+𝒔𝒊𝒏𝐀) ) / (𝐜𝐨𝐬 𝐀)  )  − 𝟏

TRIGONOMETRICAL IDENTITIES - PART - 07

13. sin⁴A – cos⁴A = 2 sin²A – 1

14. (1 – tan A)² + (1 + tan A)² = 2 sec² A

TRIGONOMETRICAL IDENTITIES - PART - 06

11. (cos A cot A) / (1 – sin A) = 1 + cosec A

12. (cot A +tan B) / (cot B + tan A) = cot A tan B

DAILY TEN WORDS - HIGH-FREQUENCY WORDS IN ENGLISH - A - LIST - COMPILED BY ZENMURALI

671. avuncular (adj) மாமனை சார்ந்த, பெற்றோரின் உடன்பிறந்தவரைச் சார்ந்த

like or for an uncle, esp. in manner, resembling a uncle in kindness or indulgence [n – avuncularity, adv – avuncluarly]

# Most 'happy' employees look at their boss as an avuncular.

672. await (v) எதிர்பார்த்துக் காத்திரு, எதிர்நோக்கு

look forward to the probable occurrence of

# The audience awaited the arrival of the chief guest.

673. awake (v) விழி, உறக்கத்தினின்று எழுப்பு

to arouse, as emotion, interest, or the like [adj – awake]

# Arise awake and stop not till the goal is reached.

Ant. unaware, sleep, unmindful

674. awaken (v) எழுப்பு, தூண்டு

cause to become awake or conscious, stop sleeping, make aware [adv – awakeningly, n – awakening]

# The parents were awakened by the crying baby in the midnight.

Ant. go to sleep, quite, dull, check

675. awe (n) பயப்படுத்து, பக்திபூர்வமான பயம்,

பயபக்தி

reverential fear or wonder [v – awe]

# His paintings have awed and amazed the public for half a century.

Ant. contempt, scorn, disrespect, disdain

676. aweary (adj) களைத்துப் போன

physically and mentally fatigued

# The late-night games make the cricketers aweary.

677. awesome (adj) அச்சமூட்டுகிற

inspiring awe or admiration or wonder, dreaded [n – awesomeness, adv – awesomely]

# The sight of a tiger is awesome.

Ant. unamazing

678. awful (adj) அச்சம் தருகிற

very bad or unpleasant [n – awfulness, adv – awfully]

# He felt awful to have missed the World cup football match final due to power failure.

Ant. good, fine, wonderful beautiful likable

679. awkward (adj) விகாரமான

causing inconvenience, lacking grace or skill in manner or movement or performance, difficult to handle or manage especially because of shape [n – awkwardness, adv – awkwardly]

# There was an awkward silence in the hospital.

Ant. pleasant, graceful, effortless, skillful

680. awl (n) குத்தூசி

a small tool for piercing holes, a pointed tool for marking surfaces or for punching small holes

# He was playing in his father's workshop with an awl.

TRIGONOMETRICAL IDENTITIES - PART - 05

9. 1 / (tan A + cot A) = cos A Sin A

10. tan A – cot A = (1 – 2 cos²A  ) / (sin A cos A)

TRIGONOMETRICAL IDENTITIES - PART - 04

7. (sin A ) / (1 + cos A) + (1 + cos A) / (sin A) = 2 cosec A

8. (1 + cos A) / (1  –  cos A) = (cosec A + cot A)²

TRIGONOMETRICAL IDENTITIES - PART - 03

TRIGONOMETRICAL IDENTITIES - PART - 02

TRIGONOMETRICAL IDENTITIES - PART - 01

DAILY TEN WORDS - HIGH-FREQUENCY WORDS IN ENGLISH - A - LIST - COMPILED BY ZENMURALI

661. avert (v) தவிர், விலக்கு

to turn away or aside [n – averting, adj – avertable]

# It is impossible to avert a natural disaster.

Ant. hold steady, allow, permit, let

662. avian (n) பறவை, போர்த்துறை வானுர்தி

pertaining to or characteristic of birds

# Avian flu is threatening the society now and then.

663. avionics (n) பறமின்னணுவியல், வான் பயண 
மின்னணுவியல்

avionics is the science of electronics used in aviation

# My uncle joined a military avionics program serving tours during operation Iraqi freedom.

664. aviary (n) பறவைக்கூடு, பறவை கூண்டு

a spacious cage or enclosure in which live birds are kept

# Children give much importance to aviary than the birds.


665. aviation (n) வான் பயணவியல்

science or practice of flying of aircraft [adj – aviatic, v – aviate]

# Wright brothers are considered as the fathers of aviation.

666. avid (adj) ஆர்வமுடைய

eager, greedy [n – avidity, adj – avidly]

# Children are generally avid to watch cartoon network.

Ant. indifferent, unwilling, disdainful

667. avocation (n) துணைத்தொழில், துணைகாரியம்

an auxiliary activity, diversion [adj – avocational, adv – avocationally]
# My avocations are painting and gardening.

Ant. vocation, occupation, work, business

668. avoidance (n) தவிர்ப்பு,  தவிர்த்தல்

deliberately avoiding; keeping away from or preventing from happening [adj – avoidable, v – avoid, adv – avoidably]

# Avoidance of non-vegetarian food is good for health.

Ant. search, invitation, facing

669. avouch (v) உறுதிமொழி கொடு

admit openly and bluntly, guarantee, attest [n – avouching, avouchment]

# The student avouched that he was involved in ragging.

Ant. deny, recant, disclaim, disavow

670. avow (v) ஒப்புக்கொள்

formal declare or confess [n – avowal, adj – avowed, adv – avowedly]

# He avowed his love to his girlfriend.

Ant. disavow, disclaim, deny, keep secret

TRIGONOMETRICAL RATIOS - PART – 10 - 100 PROBLEMS

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651. auxiliary (adj) துணையான

one who or that which aids or helps, especially when regarded as subsidiary or accessory

# Hand brake in the car is termed as an auxiliary brake.

Ant. main body, primary

652. avail (v) பயன்படுத்திக்கொள்

help, be of use, make use of, profit by [n – availing, adv – availingly]

# The principal advised the students to avail every opportunity to earn a scholarship.

Ant. be useless, detriment, disadvantages, disservice, hinder

653. avalanche (n) பனிப்பாறைச்சரிவு, பனிப்பாறைப் பெயர்ச்சி

the fall or sliding of a mass of snow or ice down a mountain-slope, often bearing with it rock [v – avalanche]

# As the train arrived there was an avalanche of passengers trying to enter.

Ant. scantiness, dearth, lack, insufficiency

654. avarice (n) பேராசை

extreme greed for wealth [adj – avaricious, adv – avariciously]

# Avarice is the cause for misery.

Ant.  generosity, benevolence, magnanimity, unselfishness

655. avant-grade (n) ஒரு குறிப்பிட்ட துறையில் புதுமையையும், புது யுத்திகளையும் மற்றும் தொழில் நுட்ப த்தையும் செயல்படுத்தும் குழு

any creative group active in the innovation and application of new concepts and techniques in a given field (especially in the arts) [adj – avant-grade]

# The Rome city celebrates its avant-grade architecture and design.

656. avatar (n) அவதாரம், திருவுரு

incarnation, descent of a deity etc. to earth in bodily form

# Buddha is considered as an avatar of Vishnu.

657. avenge (v) பழிதீர், பழிக்குப் பழி வாங்கு

inflict retribution on behalf, take vengeance for an injury [n – avenging, adj – avengeful, adv – avengingly]

# Uddham Singh (Who assassinated General O’dwyer) was the man who "avenged" the massacre at Jallianwala Bagh.

Ant. excuse, forgive, accept

658. avenue (n) நிழற்சாலை, கவின்பாதை பக்கங்களில் மரங்களுள்ள சாலை

a line of approach, broad esp. tree-lined road or street, boulevards

# Civil engineering graduates have many job avenues in future.

Ant. alley, lane

659. aver (v) உண்மையென அறிவி, உறுதி செய்

to assert as a fact, declare, state [n – averment]

# The teacher averred that the CAT examination was the toughest to the students.

Ant. deny, disavow, doubt, be uncertain

660. aversion (n) வெறுப்ப, அருவருக்கத்தக்க

a mental condition of fixed opposition to or dislike of some particular thing [adj – averse, adv – aversely]
# My sister had an aversion towards wearing jeans.

Ant. agreeable, amenable, favourable, avid