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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 17

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 17

Answers (1)

Answer:

                1

Hint:

You must know the rules of inverse trigonometric function.

Given:

\tan\left [ \cos^{-1}\left \{ \sin\left ( \cot^{-1} 1\right ) \right \} \right ]

Solution:

                \tan\left [ \cos^{-1}\left \{ \sin\left ( \cot^{-1} 1\right ) \right \} \right ]                                                        \left [ \cot^{-1}1=\cot^{-1}\left ( \cot\frac{\pi}{4} \right )=\frac{\pi}{4}\right ]               

                =\tan\left [ \cos^{-1}\left \{ \sin\left ( \frac{\pi}{4}\right ) \right \} \right ]

                =\tan\left [ \cos^{-1}\left ( \frac{1}{\sqrt2} \right ) \right ]

                =\tan\left [ \frac{\pi}{4} \right ]

                =1

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