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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions2 Marks
Question
Write the function in the simplest form: $\tan ^{-1}\left(\frac{\cos x-\sin x}{\cos x+\sin x}\right),-\frac{\pi}{4}<x<\frac{3\pi}{4}$
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Answer

We have,
$\tan ^{-1}\left(\frac{\cos x-\sin x}{\cos x+\sin x}\right)$
$=\tan ^{-1}\left(\frac{1-\tan x}{1+\tan x}\right)$
$=\tan ^{-1}\left\{\tan \left(\frac{\pi}{4}-x\right)\right\}$
$=\frac{\pi}{4}-x$

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