Prove the following results: 2sin^-1 3/5 = tan^-1(24/7)

Question

Prove the following results:

2sin^-1\(\frac 35\) = tan^-1(\(\frac{24}7\))

Answer 1

Given:- 2sin^-1\(\frac 35\) = tan^-1(\(\frac{24}7\))

Take

LHS

= 2 sin^-1\(\frac 35\)

We know that, Formula

sin^-1(x) = tan^-1(\(\frac{x}{\sqrt{1-x^2}}\))

Thus,

= RHS

So,

2 sin^-1\(\frac 35\) = tan^-1(\(\frac{27}7\))

Hence Proved