How do you prove $(1+ cosx)/(sinx + tanx)=(1 + cos2x )/ sin2x$ ?

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Answer 1 · 2015-05-02T02:27:11

Left side: $(1 + cos x)/(sin x + tan x)$ =

= $[cos x.(1 + cos x)]/[sin x(1 + cos x)]$ = $cos x/sin x = cot x$

Right side: $(1+ cos 2x)/sin^2 x$ = $(2cos^2 x)/(2.sin x. cos x)$ =

= $cos x/sin x = cot x$

Finally, left side = right side.

How do you prove (1+ cosx)/(sinx + tanx)=(1 + cos2x )/ sin2x(1+ cosx)/(sinx + tanx)=(1 + cos2x )/ sin2x?