If y = 1/2 log (1-cos 2x / 1 + cos 2x), prove that dy/dx = 2 cosec 2x

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If y = 1/2 log (1-cos 2x / 1 + cos 2x), prove that dy/dx = 2 cosec
2x

Rishabh Mittal · Accepted Answer

y=12 log 1-cos 2x1 + cos 2x  =12 log 2 sin2x2 cos2x=12 log tan2x  =log tan2x12=logtan xy= log tan xOn differentiating both sides wrt x , we gety'=1tan xsec2x=cos xsin x1cos2x    =1sin x cos x=22 sin x cos x    =2sin 2x=2 cosec 2x Hence Proved