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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 23

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 23

Answers (1)

Answer:

                \frac{\pi}{4}

Hint:

You must know the sum of three angles of s triangle and inverse trigonometric function.

Given:

                \tan^{-1}2 and  \tan^{-1}3 are measures of two angles of a triangle, find the third angle.

Solution:

Given two angles are \tan^{-1}2 and  \tan^{-1}3

Let third angle be \theta

                \tan^{-1}2+\tan^{-1}3+\theta=180^{\circ}

         \Rightarrow \tan^{-1}\left ( \frac{2+3}{1-2\left ( 3 \right )} \right )=180^{\circ}-\theta                                               \left [ \because \tan^{-1}a+\tan^{-1}b=\tan^{-1}\left ( \frac{a+b}{1-ab} \right ) \right ]

       \Rightarrow \left (\frac{5}{-5} \right )=\tan\left ( 180-\theta^{\circ} \right )

         \Rightarrow-1=-\tan\theta

         \Rightarrow1=\tan\theta

         \Rightarrow\tan\frac{\pi}{4}=\tan\theta

         \Rightarrow\theta=\frac{\pi}{4}

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