If y = tan^{-1}left(frac{a cos x - b sin x}{b | vedclass

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(C) Given $y = 	an^{-1}\left(\frac{a \cos x - b \sin x}{b \cos x + a \sin x}ight)$.Divide the numerator and denominator by $b \cos x$:$y = 	an^{-1

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$-1$

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(C) Given $y = 	an^{-1}\left(\frac{a \cos x - b \sin x}{b \cos x + a \sin x}ight)$.Divide the numerator and denominator by $b \cos x$:$y = 	an^{-1}\left(\frac{\frac{a}{b} - 	an x}{1 + \frac{a}{b} 	an x}ight)$.Let $\frac{a}{b} = 	an 	heta$,where $	heta = 	an^{-1}(\frac{a}{b})$.Then $y = 	an^{-1}\left(\frac{	an 	heta - 	an x}{1 + 	an 	heta 	an x}ight)$.Using the formula $	an(A - B) = \frac{	an A - 	an B}{1 + 	an A 	an B}$,we get:$y = 	an^{-1}(	an(	heta - x)) = 	heta - x$.Since $	heta = 	an^{-1}(\frac{a}{b})$ is a constant,its derivative is $0$.Therefore,$\frac{dy}{dx} = \frac{d}{dx}(	heta - x) = 0 - 1 = -1$.

If $y = \tan^{-1}\left(\frac{a \cos x - b \sin x}{b \cos x + a \sin x}\right)$,then $\frac{dy}{dx}$ is equal to

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