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Find the principal value of \begin{align} cosec^{-1}\left({-\sqrt2}\ri...

Find the principal value of egin{align | Class 12 Mathematics Chapter Inverse Trigonometric Functions, Inverse Trigonometric Functions NCERT Solutions

Question: Find the principal value of \begin{align} cosec^{-1}\left({-\sqrt2}\right)\end{align}

Answer:

\begin{align} Let \;\; cosec^{-1}\left({-\sqrt2}\right)=y \;\;Then\;\; cosec y = -{\sqrt2} =- cosec\left(\frac{\pi}{4}\right) = cosec\left(-\frac{\pi}{4}\right)\end{align}

We know that the range of the principal value branch of cosec⁻¹ is

\begin{align} \left[-\frac{\pi}{2},\frac{\pi}{2}\right] - \left(0 \right) and \;\;cosec\left(-\frac{\pi}{4}\right) = -\sqrt2.\end{align}

Therefore, the principal value of

\begin{align} cosec^{-1}\left(-\sqrt2\right) is -\frac{\pi}{4}\end{align}

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Popular questions of class 12 Mathematics

Q: Given an example of a relation. Which is
(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
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(iv) Relation R in the set Z of all integers defined as
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Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about Inverse Trigonometric Functions.
Review previous year question papers to get an idea of how such questions may be framed in exams.
Practice answering questions within the time limit to improve your speed and accuracy.
Discuss your answers with your teachers or peers to get feedback and improve your understanding.

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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , Question 10: Find the principal value of egin{align} cosec^{-1}left({-sqrt2} ight)end{align}....

Find the principal value of egin{align | Class 12 Mathematics Chapter Inverse Trigonometric Functions, Inverse Trigonometric Functions NCERT Solutions

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Find the principal value of egin{align | Class 12 Mathematics Chapter Inverse Trigonometric Functions, Inverse Trigonometric Functions NCERT Solutions