# Prove that 2 sin ^{-1} 3/5 = tan^{- 1} 24/7

**Solution:**

Inverse trigonometric functions are the inverse ratio of the basic trigonometric ratios.

Here the basic trigonometric function of Sin θ = y, can be changed to θ = sin^{-1} y

Let sin^{- 1} 3/5 = x

⇒ sin x = 3 / 5

Then,

cos x = 1 - (3/5)^{2}

= 4/5

Therefore,

tan x = 3/4

x = tan^{- 1} 3/4

sin^{- 1} 3/5 = tan^{- 1} 3/4 ....(1)

Thus,

LHS = 2 sin^{- 1} 3/5

= 2 tan^{- 1} 3/4 [from (1)]

= tan^{- 1} [(2 x 3/4)/(1 - (3/4)²)]

= tan^{- 1} (24/7)

= RHS

NCERT Solutions for Class 12 Maths - Chapter 2 Exercise ME Question 3

## Prove that 2sin ^{-1} 3/5 = tan^{- 1} 24/7

**Summary:**

Hence we have proved by using inverse trigonometric functions that 2 sin ^{-1} 3/5 = tan^{- 1} 24/7

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