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Question
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
Solution
L.H.S. = tan A – cot A
= `(sin A)/(cos A) - (cos A)/(sin A)`
= `(sin^2A - cos^2A)/(sin A cos A)`
= `(1 - cos^2A - cos^2A)/(sin A cos A)` ...(∵ sin2A = 1 – cos2A)
= `(1 - 2cos^2A)/(sin A cos A)`
= R.H.S.
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