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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
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
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