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Inverse Trigonometric Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSInverse Trigonometric Functions1 Mark
Question
If $f(x)=|\cos x|$, then $f\left(\frac{3 \pi}{4}\right)$ is
✓

Answer

$f(x)=|\cos x|$
At$\frac{\pi}{2} < x < \pi, \cos x<0$
$\therefore|\cos x|=-\cos x$
$ \Rightarrow f(x)=-\cos x$
$\therefore f\left(\frac{3 \pi}{4}\right)=-\cos \left(\frac{3 \pi}{4}\right)=-\cos \left(\pi-\frac{\pi}{4}\right)$
$\quad=\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}} \quad[\because \cos (\pi-\theta)=-\cos \theta]$

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