Asked by Justin
Verify the following identity: sin(x)*cos(x)*(cot(x)+tan(x))=1
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Answers
Answered by
Damon
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.
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.
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