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Q)

Differentiate w.r.t. x, $ y=\tan^{-1}\bigg[\Large\frac{a\cos x-b\sin x}{b\cos x+a \sin x}\bigg]$

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A)
Toolbox:
  • Divide number and then by b cos x
  • $ tan^{-1}\large\frac{x-y}{1+xy}=tan^{-1}x-tan^{-1}y$
$ y = tan^{-1} \bigg( \large\frac{\large\frac{a}{b}-tanx}{1+\large\frac{a}{b}tanx} \bigg)$
$ = tan^{-1}\large\frac{a}{b}-x$
$ \large\frac{dy}{dx}=-1$
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