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Provide solution for RD Sharma math class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 30

Answers (1)

Answer: \frac{3 \pi}{4}

Given: \cos ^{-1}\left(\cos \frac{5 \pi}{4}\right)

Hint: Try to solve \cos  function first.


          \cos ^{-1}\left(\cos \frac{5 \pi}{4}\right) \neq \frac{5 \pi}{4} \ \ as \ \ \frac{5 \pi}{4}  doesn’t lie in between 0  and 5 \pi

We, have          

\cos ^{-1}\left(\cos \frac{5 \pi}{4}\right)=\cos ^{-1}\left\{\cos \left(2 \pi-\frac{3 \pi}{4}\right)\right\}

                                        \begin{array}{l} =\cos ^{-1}\left\{\cos \left(\frac{3 \pi}{4}\right)\right\} \\\\ =\frac{3 \pi}{4} \end{array}

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