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(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x

User Shamon
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1 Answer

7 votes
As


\tan x=(\sin x)/(\cos x)

\cot x=(\cos x)/(\sin x)

we have


\sin x(\tan x\cos x-\cot x\cos x)=\sin x\left(\sin x-(\cos^2x)/(\sin x)\right)=\sin^2x-\cos^2x

Recalling that
\cos2x=\cos^2x-\sin^2x, we end up with


-\cos2x=1-2\cos2x

1=\cos2x

\implies2x=2n\pi

(where
n is any integer)


\implies x=n\pi
User Gotson
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8.8k points