If \sin^{-1}\left ( \frac{3}{x} \right )+\sin^{-1}\left ( \frac{4}{x} \right )=\frac{\pi }{2} then find the value of x.

 

 

 

 
 
 
 
 

Answers (1)

Let \sin^{-1}\left ( \frac{3}{x} \right )=A and \sin^{-1}\left ( \frac{4}{x} \right )=B

A+B=\frac{\pi}{2}\Rightarrow A=\frac{\pi}{2}-B

\sin A=\sin \left (\frac{\pi}{2}-B \right )=\cos B

\cos B = \sqrt{1-\sin^2 B}     

    \frac{3}{x}=\sqrt{1-\frac{16}{x^2}}

Taking square on both sides

\frac{9}{x^2}={1-\frac{16}{x^2}}

\frac{9}{x^2} + \frac{16}{x^2}=1\Rightarrow \frac{25}{x^2}=1

x^2=25\Rightarrow x=\pm 5\: \: \: x=5

 

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout NEET May 2022

An exhaustive E-learning program for the complete preparation of NEET..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions