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Write the Following in the Simplest Form: `Tan^-1sqrt((A-x)/(A+X)),-a<X<A` - Mathematics

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Question

Write the following in the simplest form:

`tan^-1sqrt((a-x)/(a+x)),-a<x<a`

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Solution

Let `x = acos theta`

Now,

`tan^-1sqrt((a-x)/(a+x))=tan^-1sqrt((a-acostheta)/(a+acostheta))`

`=tan^-1sqrt((1-costheta)/(1+costheta))`

`=tan^-1sqrt((2sin^2  theta/2)/(2cos^2  theta/2))`

`=tan^-1(tan  theta/2)`

`=theta/2`

`=1/2cos^-1(x/a)`

`thereforetan^-1sqrt((a-x)/(a+x))=(cos^-1(x/a))/2`

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Chapter 4: Inverse Trigonometric Functions - Exercise 4.07 [Page 43]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 4 Inverse Trigonometric Functions
Exercise 4.07 | Q 7.06 | Page 43

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