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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 4

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 4

Answers (1)

Answer:

                \frac{3\pi}{10}

Hint:

You must know the rules of trigonometric and inverse trigonometric function.

Given:

\sin^{-1}x=\frac{\pi}{5} for some x\: \epsilon \left ( -1,1 \right ), find the value of \cos^{-1}x.

Solution:

Inverse trigonometric rule,

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

\Rightarrow         \frac{\pi}{5}+cos^{-1}x=\frac{\pi}{2}

\Rightarrow         cos^{-1}x=\frac{\pi}{2}-\frac{\pi}{5}

\Rightarrow         cos^{-1}x=\frac{5\pi-2\pi}{10}

\Rightarrow         cos^{-1}x=\frac{3\pi}{10}

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