Answered: "Verify the identity tan×csc2x–tan⁡x=cot⁡"

avissidep

Answered question

2021-09-06

Verify the identity

\tan \times \csc^{2} x - \tan x = \cot

Layton

Skilled2021-09-07Added 89 answers

\tan \times \csc^{2} x - \tan x =

= \tan x \times \frac{1}{\sin^{2} x} - \tan x =

= \frac{\sin x \times 1}{\cos x \times \sin^{2} x} - \frac{\sin x}{\cos x} =

= \frac{1}{\sin x \times \cos x} - \frac{\sin x}{\cos x} =

= \frac{1 - \sin^{2} x}{\sin x \times \cos x} = \frac{\cos^{2} x}{\sin x \times \cos x} = \frac{\cos x}{\sin x} = \cot x

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