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Question
Prove the following identities:
tan2 A – sin2 A = tan2 A . sin2 A
Sum
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Solution
L.H.S. = tan2 A – sin2 A
= `sin^2A/cos^2A - sin^2A/1`
= `(sin^2A - sin^2A cos^2A)/(cos^2A)`
= `(sin^2A(1 - cos^2A))/cos^2A`
= `sin^2A/cos^2A (1 - cos^2A)`
= tan2 A sin2 A ...(∵ 1 – cos2 A = sin2 A)
= R.H.S.
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