x-cot-1-cos-tan-1-cos-sin-x-

Question Number 161181 by cortano last updated on 13/Dec/21

x = \cot^{- 1} (\sqrt{\cos θ}) - \tan^{- 1} (\sqrt{\cos θ})

\sin x = ?

Commented by MJS_new last updated on 13/Dec/21

\sin (\arctan a - \arctan b) = \frac{a - b}{\sqrt{(a^{2} + 1) (b^{2} + 1)}}

arccot (r) = \frac{1}{\arctan r} \Rightarrow a = \frac{1}{b}

\Rightarrow

\frac{a - b}{\sqrt{(a^{2} + 1) (b^{2} + 1)}} = \frac{1 - b^{2}}{1 + b^{2}}

\Rightarrow

answer is \frac{1 - \cos θ}{1 + \cos θ}

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