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Prove the following identities: sec^2θ – (sin^2θ – 2sin^4θ)/(2cos^4θ – cos^2θ) = 1

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Question

Prove the following identities:

`sec^2θ - (sin^2θ - 2sin^4θ)/(2cos^4θ - cos^2θ) = 1`

Theorem
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Solution

LHS = `(1 + tan^2θ) - (sin^2θ(1 - 2sin^2θ))/(cos^2θ(2cos^2θ - 1))`

= (1 + tan2θ) – tan2θ   ...[∵ 1 – 2 sin2θ = 2 cos2θ – 1 = 1 – cos 2θ]

= 1 = RHS.

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Chapter 13: Trigonometric identities - EXERCISE 13A [Page 617]

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R.S. Aggarwal Mathematics [English] Class 10
Chapter 13 Trigonometric identities
EXERCISE 13A | Q 14. | Page 617
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