# Solve the equation tan x sec x sin x= tan^{2}x

Solve the equation $$\tan x \sec x \sin x= \tan^{2}x$$

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joshyoung05M
Work int the left side. By reciprocal identities, $$\sec x=1/\cos x$$ so:
$$\tan x\sec x\sin x=\tan x\times\frac{1}{\cos x}\times\sin x$$
$$\tan x\sec x\sin x=\tan x\times\frac{\sin x}{\cos x}$$
By quotient identity, $$\tan x=\frac{\sin x}{\cos x}$$ so:
$$\tan x\sec x\sin x=\tan x\times\tan x$$
$$\tan x\sec x\sin x=\tan^{2}x$$