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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 1

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 1

Answers (1)

Answer: 15

Hint:

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

Given:

                \sec^{2}\left ( \tan^{-1} 2\right )+cosec^{2}\left ( \cot^{-1}3 \right )

Solution:

                \sec^{2}\left ( \tan^{-1} 2\right )+cosec^{2}\left ( \cot^{-1}3 \right )

           \left[\therefore \sec ^{2}x=1+\tan ^{2}x \: \ \&\: \ cosec ^{2}x=1+\cot^{2}x \right ]

                =1+\tan^{2}\left ( \tan^{-1}2 \right )+1+\cot^{2}\left ( \cot^{-1} 3\right )            

                =1+\left [ \tan\left ( \tan^{-1}2 \right ) \right ]^{2}+1+\left [ \cot\left ( \cot^{-1}3 \right ) \right ]^{2}

                =1+\left [ 2 \right ]^{2}+1+\left [ 3 \right ]^{2}

                =1+4+1+9

                =15

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