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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 12

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 12

Answers (1)

Answer:

                \frac{1}{\sqrt2}

Hint:

You must know the rules of inverse trigonometric function.

Given:

3\sin^{-1}x=\pi-\cos^{-1}x, then find x

Solution:

                3\sin^{-1}x=\pi-\cos^{-1}x

\Rightarrow         3\sin^{-1}x=\pi-\left [ \frac{-\pi}{2}-\sin^{-1} x\right ]

\Rightarrow         3\sin^{-1}x=\pi- \frac{\pi}{2}+\sin^{-1} x

\Rightarrow         3\sin^{-1}x-\sin^{-1} x=\frac{2\pi-\pi}{2}

\Rightarrow         2\sin^{-1}x=\frac{\pi}{2}

\Rightarrow         \sin^{-1}x=\frac{\pi}{4}

\Rightarrow         x=\sin\left (\frac{\pi}{4} \right )

\Rightarrow         x=\frac{1}{\sqrt{2}}

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