Value of tan ^{-1}left(frac{sin 2-1}{cos 2}ri | vedclass

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(B) Given expression is $	an ^{-1}\left(\frac{\sin 2-1}{\cos 2}ight)$.Using the identities $\sin 2 = 2\sin 1 \cos 1$,$1 = \sin^2 1 + \cos^2 1$,and

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$1-\frac{\pi}{4}$

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(B) Given expression is $	an ^{-1}\left(\frac{\sin 2-1}{\cos 2}ight)$.Using the identities $\sin 2 = 2\sin 1 \cos 1$,$1 = \sin^2 1 + \cos^2 1$,and $\cos 2 = \cos^2 1 - \sin^2 1$:$\frac{\sin 2 - 1}{\cos 2} = \frac{2\sin 1 \cos 1 - (\sin^2 1 + \cos^2 1)}{\cos^2 1 - \sin^2 1} = \frac{-(\cos 1 - \sin 1)^2}{(\cos 1 - \sin 1)(\cos 1 + \sin 1)}$.Since $\cos 1 > \sin 1$ (as $1 	ext{ radian} \approx 57.3^\circ$),we can simplify this to $\frac{-(\cos 1 - \sin 1)}{\cos 1 + \sin 1} = \frac{\sin 1 - \cos 1}{\cos 1 + \sin 1}$.Dividing numerator and denominator by $\cos 1$,we get $\frac{	an 1 - 1}{1 + 	an 1} = 	an(1 - \frac{\pi}{4})$.Thus,$	an ^{-1}(	an(1 - \frac{\pi}{4})) = 1 - \frac{\pi}{4}$.

Value of $\tan ^{-1}\left(\frac{\sin 2-1}{\cos 2}\right)$ is

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