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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 24

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 24

Answers (1)

Answer:

                \sqrt{ab}

Hint:

You must know the rules of inverse trigonometric function.

Given:

                \tan^{-1}\frac{a}{x}+\tan^{-1}\frac{b}{x}=\frac{\pi}{2}

Solution:

As we know that,

            \tan^{-1}x+\cot^{-1}x=\frac{\pi}{2}

       \Rightarrow \frac{a}{x}=\frac{\pi}{2}-\frac{a}{x}                                                                                              …….. (i)                      

  Substituting the values on equation, we get

       \Rightarrow \frac{\pi}{2}-\frac{a}{x} +\frac{b}{x} =\frac{\pi}{2}

      \Rightarrow \frac{b}{x} =\frac{a}{x}

      \Rightarrow \frac{b}{x} =\frac{x}{a}

      \Rightarrow \frac{b}{x} =\frac{x}{a}

       \Rightarrow x^{2}=ab

       \Rightarrow x=\pm \sqrt{ab}

 

Posted by

infoexpert27

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