Value of tan^{-1} (frac{sin2 -1}{cos2}) is equal to:-

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3.Trigonometrical Ratios, Functions and Identities

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The value of $tan^{-1} (\frac{sin2 -1}{cos2})$ is equal to:-

A

$\frac{\pi}{2} - 1$

B

$2 - \frac{\pi}{2}$

C

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

D

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

Solution

$\tan ^{-1}\left[\frac{2 \sin 1 \cos 1-\cos ^{2} 1-\sin ^{2} 1}{\cos ^{2} 1-\sin ^{2} 1}\right]$

$=-\tan ^{-1} \frac{\cos 1-\sin 1}{\cos 1+\sin 1}$

$=-\tan ^{-1} \tan \left[\frac{\pi}{4}-1\right]$

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

Standard 11

Mathematics

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