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

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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