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Question
Prove the following:
tan2θ − sin2θ = sin4θ sec2θ
Solution
L.H.S. = tan2θ − sin2θ
= `sin^2theta/cos^2theta - sin^2theta`
= `sin^2theta (1/cos^2theta - 1)`
= `(sin^2theta(1 - cos^2theta))/cos^2theta`
= (sin2θ) (sin2θ) sec2θ
= sin4θ sec2θ
= R.H.S.
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