Write the function in the simplest form: tan | vedclass

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

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$\frac{\pi}{4}-x$

Vedclass · Answer

(C) Given expression: $	an ^{-1}\left(\frac{\cos x-\sin x}{\cos x+\sin x}ight)$Divide the numerator and denominator by $\cos x$:$= 	an ^{-1}\left(\frac{\frac{\cos x}{\cos x}-\frac{\sin x}{\cos x}}{\frac{\cos x}{\cos x}+\frac{\sin x}{\cos x}}ight)$$= 	an ^{-1}\left(\frac{1-	an x}{1+	an x}ight)$Using the formula $	an(A-B) = \frac{	an A - 	an B}{1 + 	an A 	an B}$,where $A = \frac{\pi}{4}$ and $B = x$:$= 	an ^{-1}\left(	an\left(\frac{\pi}{4}-xight)ight)$$= \frac{\pi}{4}-x$

Write the function in the simplest form: $\tan ^{-1}\left(\frac{\cos x-\sin x}{\cos x+\sin x}\right)$

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