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Question Number 182848 by malithxd last updated on 15/Dec/22

\frac{{s i n}^{3} x - s i n x + c o s x}{s i n x} = c o t x - {c o s}^{2} x

p r o v e t h i s

Answered by Rasheed.Sindhi last updated on 15/Dec/22

\frac{{s i n}^{3} x - s i n x + c o s x}{s i n x} = c o t x - {c o s}^{2} x

L H S : \sin^{2} x - 1 + \frac{\cos x}{\sin x}

= - (1 - \sin^{2} x) + \frac{\cos x}{\sin x}

- \cos^{2} x + \cot x = R H S

Answered by manxsol last updated on 15/Dec/22

/ s i n x

{s i n}^{2} - 1 + c t x

- {c o s}^{2} + c o t x = c o t x - {c o s}^{2} x

Answered by cortano1 last updated on 15/Dec/22

\frac{\sin^{3} x - \sin x + \cos x}{\sin x}

= \frac{\sin x (\sin^{2} x - 1) + \cos x}{\sin x}

= \sin^{2} x - 1 + \cot x

= - \cos^{2} x + \cot x

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