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INVERSE TRIGNOMETRIC FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSINVERSE TRIGNOMETRIC FUNCTIONS2 Marks
Question
Find the principal values:
 $\tan^{-1}\left(1\right)+\cos^{-1}\bigg(-\frac{1}{2}\bigg)+\sin^{-1}\bigg(-\frac{1}{2}\bigg)$
✓

Answer

$ \tan^{-1}\left(1\right)+\cos^{-1}\bigg(\frac{-1}{2}\bigg)+\sin^{-1}\bigg(\frac{-1}{2}\bigg)$ $=\tan^{-1}\tan\frac{\pi}{4}+\cos^{-1}\bigg(-\cos\frac{\pi}{3}\bigg)+\sin^{-1}\bigg(-\sin\frac{\pi}{6}\bigg)$
$=\frac{\pi}{4}+\cos\bigg({\pi}-\frac{\pi}{3}\bigg)+\sin^{-1}\sin\bigg(-\frac{\pi}{6}\bigg)=\frac{\pi}{4}+\frac{2\pi}{3}-\frac{\pi}{6}$
$=\frac{3\pi+8\pi-2\pi}{12}=\frac{9\pi}{12}=\frac{3\pi}{4}$

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