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Inverse Trigonometric Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSInverse Trigonometric Functions2 Marks
Question
Write $\cot^{-1} \left(\frac{1}{\sqrt{x^{2}-1}}\right), x>1$ in the simplest form.
✓

Answer

Let $x= \sec \theta,$
then $\sqrt{x^{2}-1}=\sqrt{\sec ^{2} \theta-1} = \tan \theta$
Therefore, $\cot ^{-1} \frac{1}{\sqrt{x^{2}-1}}=\cot ^{-1}(\cot \theta)=\theta=\sec ^{-1} x ,$ is the simplest form.

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