Question #62f68

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Answer 1 · 2017-03-15T04:57:24

see explanation below

Let we take RHS to prove LHS

$(1 -sin 2 x)/ cos (2 x) = (sin^2 x + cos ^2 x - 2sin x cos x)/(cos^2 x -sin^2 x)$

$= (sin x - cos x)^2/((cos x - sin x)(cos x + sin x))$

$= (sin x - cos x)^2/(-(-cos x + sin x)(cos x + sin x))$

$=- (sin x - cos x)^cancel 2/(cancel(( sin x - cos x))(cos x + sin x))$

$=- (sin x - cos x)/(cos x + sin x) = (cos x - sin x)/(cos x + sin x)$

divided by $sin x$

$(cos x/sin x - sin x/sin x)/(cos x/sin x + sin x/sin x) = (cost x - 1)/(cot x + 1)$