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  • Provide solution for RD Sharma math class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 14

Provide solution for RD Sharma math class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 14

Answers (1)

Answer: 60^{\circ}

Given:

\sin ^{-1}\left(\sin \left(-600^{\circ}\right)\right)

Hint:

\sin x=\sin (\pi-x)

Solution:       

\begin{array}{l} \sin ^{-1}\{\sin x\}=x \\ \end{array}

 

\begin{aligned} \begin{array}{l} \sin ^{-1}\left\{\sin \left(600^{\circ}\right)\right\} =\sin ^{-1}\left\{\sin \left(720^{\circ}-600^{\circ}\right)\right\} \\ \end{array} \end{aligned}

                                           \begin{aligned} \begin{array}{l} =\sin ^{-1}\left\{\sin \left(120^{\circ}\right)\right\} \\ =\sin ^{-1}\left\{\sin \left(180^{\circ}-120^{\circ}\right)\right\} \\ =\sin ^{-1}\left\{\sin \left(60^{\circ}\right)\right\}=60^{\circ}\\ \ \\ \end{array} \end{aligned} 

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