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  • explain solution RD Sharma class 12 chapter Inverse Trignometric Functions exercise 3.7 question 1 sub question (viii) maths

explain solution RD Sharma class 12 chapter Inverse Trignometric Functions exercise 3.7 question 1 sub question (viii) maths

Answers (1)

Answer:   \pi -4

Hint: The principal value branch of function  \sin ^{-1}  is  \left [ -\frac{\pi }{2},\frac{\pi }{2} \right ]

Given:   \sin ^{-1}(\sin 4)

Explanation:

We know that \sin ^{-1}(\sin x)=x \text { with } x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]  which is approximately equal to [-1.57, 1.57]

But x=4 , which do not lie on the above range

We know,

                \begin{aligned} &\sin (\pi-x)=\sin (x) \\ &\sin (\pi-4)=\sin (4) \text { also } \pi-4 \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \\ &\sin ^{-1}(\sin 4)=\sin ^{-1}(\sin \pi-4) \end{aligned}

Then,

                \sin ^{-1}(\sin \pi-4)=\pi-4

 

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