Verify the identity&nbsp;tan×csc2x–tanx=cotx

tan×csc2x–tan⁡x= =tan⁡x×1sin2x–tan⁡x= =sin⁡x×1cos⁡x×sin2x–sin⁡xcos⁡x= =1sin⁡x×cos⁡x–sin⁡xcos⁡x= =1–sin2xsin⁡x×cos⁡x=cos2xsin⁡x×cos⁡x=cos⁡xsin⁡x=cot⁡x

Answered: "Verify the identitytan×csc2x–tanx=cotx"

Paulkenyo

2022-08-17

Verify the identity $\tan \times \csc^{2} x - tanx = \cot x$

hrikalegt15

Beginner2022-08-18Added 11 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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