Class 12 Mathematics Inverse Trigonometric Functions Introduction to inverse trigonometric functions Easy Level 33

(\cos^{-1}\left\(-\frac{1}{\sqrt{2}}\right\)) का मान क्या है?

What is the value of (\cos^{-1}\left\(-\frac{1}{\sqrt{2}}\right\))?

Author: Muft Shiksha Editorial Team Published:
Explanation opens after your attempt
Correct Answer

A. \(\frac{3\pi}{4}\)

Step 1

Concept

Because \(\cos\frac{3\pi}{4}=-\frac{1}{\sqrt{2}}\) and \(\frac{3\pi}{4}\in[0,\pi]\). For \(\cos^{-1}\), do not take a negative principal value.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{3\pi}{4}\). Because \(\cos\frac{3\pi}{4}=-\frac{1}{\sqrt{2}}\) and \(\frac{3\pi}{4}\in[0,\pi]\). For \(\cos^{-1}\), do not take a negative principal value.

Step 3

Exam Tip

क्योंकि \(\cos\frac{3\pi}{4}=-\frac{1}{\sqrt{2}}\) और \(\frac{3\pi}{4}\in[0,\pi]\) है। \(\cos^{-1}\) में प्रधान मान ऋणात्मक नहीं लेते।

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Mathematics Answer, Explanation and Revision Hints

(\cos^{-1}\left\(-\frac{1}{\sqrt{2}}\right\)) का मान क्या है? / What is the value of (\cos^{-1}\left\(-\frac{1}{\sqrt{2}}\right\))?

Correct Answer: A. \(\frac{3\pi}{4}\). Explanation: क्योंकि \(\cos\frac{3\pi}{4}=-\frac{1}{\sqrt{2}}\) और \(\frac{3\pi}{4}\in[0,\pi]\) है। \(\cos^{-1}\) में प्रधान मान ऋणात्मक नहीं लेते। / Because \(\cos\frac{3\pi}{4}=-\frac{1}{\sqrt{2}}\) and \(\frac{3\pi}{4}\in[0,\pi]\). For \(\cos^{-1}\), do not take a negative principal value.

Which concept should I revise for this Mathematics MCQ?

Because \(\cos\frac{3\pi}{4}=-\frac{1}{\sqrt{2}}\) and \(\frac{3\pi}{4}\in[0,\pi]\). For \(\cos^{-1}\), do not take a negative principal value.

What exam hint can help solve this Mathematics question?

क्योंकि \(\cos\frac{3\pi}{4}=-\frac{1}{\sqrt{2}}\) और \(\frac{3\pi}{4}\in[0,\pi]\) है। \(\cos^{-1}\) में प्रधान मान ऋणात्मक नहीं लेते।