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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 10

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 10

Answers (1)

Answer:

                \frac{2\pi}{3}

Hint:

You must know the rules of inverse trigonometric function.

Given:

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

Solution:

We know

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

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

Adding both

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

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

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

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

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

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

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