Check the solution to "Solve the equation tan⁡xsec⁡xsin⁡x=tan2⁡x"

Joni Kenny

Answered question

2020-10-21

Solve the equation

\tan x \sec x \sin x = \tan^{2} x

joshyoung05M

Skilled2020-10-22Added 97 answers

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

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