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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 8

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 8

Answers (1)

Answer:

                1

Hint:

You must know the value of inverse trigonometric function.

Given:

\tan ^{-1}x-\tan^{-1}y=\frac{\pi}{4}, then find x-y-xy

Solution:

   \Rightarrow             \tan ^{-1}x-\tan^{-1}y=\frac{\pi}{4}

\Rightarrow         \tan^{-1}\left ( \frac{x-y}{1+xy} \right )=\frac{\pi}{4}                                                                 \left [ \because \tan^{-1}a-\tan^{-1}b=\tan^{-1}\left ( \frac{a-b}{1+ab} \right ) \right ]

\Rightarrow         \left ( \frac{x-y}{1+xy} \right )=\tan\frac{\pi}{4}

\Rightarrow         \left ( \frac{x-y}{1+xy} \right )=1

\Rightarrow         \left ( x-y \right )=1+xy

\Rightarrow         x-y-xy=1

 

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