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ML Aggarwal Solutions Class 10 Mathematics Solutions for Trigonometric Identities Exercise 18 in Chapter 18 - Trigonometric Identities
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sec4 A – tan4 A = 1 + 2 tan2 A
Answer:
Solution:
First we can apply algebraic identity as (a4 - b4 )= (a2+b2) (a2 - b2) in LHS
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.
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