Verify the following identity: sin(x)*cos(x)*(cot(x)+tan(x))=1

Question

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Answer 1

cotx = cos x/sin x
tan x = sin x/ cos x

cot x + tan x = cos x/sin x + sin x/ cos x
so
cot x + sin x = cos^2 x/sin x cos x + sin^2 x/sin x cos x

cot x + tan x = (cos^2 x+sin^2x)/sin x cos x

but cos^2 x + sin^2 x = 1
you take it from there.