Prove tan^{- 1} 2/11 + tan^{- 1} 7/24 = tan^-1 1/2

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

Since we know that

Using trigonometric identity 

tan^{- 1} x + tan^{- 1} y = tan^{- 1} (x + y) / (1 - xy)

Now,

LHS = tan^{- 1} 2/11 + tan^{- 1} 7/24

= tan^{- 1} [(2/11 + 7/24) / (1 - (2/11). (7/24)]

= tan^{- 1} [((48 + 77) / 264) / ((264 - 14) / 264)]

On simplifying the terms,

= tan^{- 1} (125 / 250)

= tan^{- 1}(1 / 2)

= RHS

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NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.2 Question 3

Prove tan^{- 1} 2/11 + tan^{- 1} 7/24 = tan^-1 1/2

Summary:

Hence we have proved that  tan^{- 1} 2/11 + tan^{- 1} 7/24 = tan^-1 1/2. Inverse trigonometric functions are the inverse ratio of the basic trigonometric ratios