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weqwewe [10]
3 years ago
15

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

Mathematics
1 answer:
Aliun [14]3 years ago
5 0
As

\tan x=\dfrac{\sin x}{\cos x}
\cot x=\dfrac{\cos x}{\sin x}

we have

\sin x(\tan x\cos x-\cot x\cos x)=\sin x\left(\sin x-\dfrac{\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
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