Advertisements
Advertisements
Question
Prove the following identities:
`sec^2θ - (sin^2θ - 2sin^4θ)/(2cos^4θ - cos^2θ) = 1`
Theorem
Advertisements
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.
shaalaa.com
Is there an error in this question or solution?
