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Question
Prove the following:
`sinx tan(x/2) + 2cosx = 2/(1 + tan^2(x/2))`
Solution
L.H.S. = `sinx tan(x/2) + 2cosx`
= `(2sin x/2 cos x/2)((sin x/2)/(cos x/2)) + 2cosx`
= `2sin^2 x/2 + 2cosx`
= 1 – cos x + 2cosx
= 1 + cos x
= `2cos^2 x/2`
= `2/(sec^2 x/2)`
= `2/(1 + tan^2 x/2)`
= R.H.S.
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