(i) (1 + tan A)/ sin A + (1 + cot A)/ cos A = 2 (sec A + cosec A) (ii) sec4 A – tan4 A = 1 + 2 tan2 A

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deepaksoniGuru

Asked: March 16, 20212021-03-16T02:10:01+05:30 2021-03-16T02:10:01+05:30In: ICSE

This is an important question from the
Book- ML Aggarwal
Board- ICSE
Publication- Avichal
Chapter- Trigonometric Identities
Chapter number-18

We have to prove that

(i) (1 + tan A)/ sin A + (1 + cot A)/ cos A = 2 (sec A + cosec A) (ii) sec4 A – tan4 A = 1 + 2 tan2 A

Trigonometric Identities, class 10th, chapter 18th, question no 25, ICSE board, ML aggarwal..

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AAREKH · Answer 1 · 2021-03-16T03:05:58+05:30

AAREKH Guru

Solution:

(ii) sec⁴ A – tan⁴ A = 1 + 2 tan² A

L.H.S. = sec⁴ A – tan⁴ A

= (sec² A – tan² A) (sec² A + tan² A)

= (1 + tan⁴ A – tan⁴ A) (1 + tan⁴ A + tan⁴ A) [As sec² A = tan⁴ A + 1]

= 1 (1 + 2 tan² A)

= 1 + 2 tan² A = R.H.S.