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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 2

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 2

Answers (1)

Answer:

                \frac{\sqrt{3}}{2}

Hint:

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

Given:

                \sin^{-1}x-\cos^{-1}x= \frac{\pi}{6}

Solution:

                \sin^{-1}x-\cos^{-1}x= \frac{\pi}{6}
\Rightarrow \frac{\pi}{2}-x-x=\frac{\pi}{6}                                                   \left [ \because \sin^{-1} x+\cos^{-1}x=\frac{\pi}{2}\right ]        

\\\Rightarrow-2\cos^{-1}x= \frac{\pi}{6}-\frac{\pi}{2}

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

\Rightarrow         \cos^{-1}x=\frac{\pi}{6}

\Rightarrow         x=\cos\frac{\pi}{6}

\Rightarrow\frac{\sqrt{3}}{2}

Posted by

infoexpert27

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