NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

The value of s i n c o t - 1 c o s c o t - 1 1 x is equal to x > 0

Options

A1 + x 2 2 + x 2
B1 - x 2 2 + x 2
C1 + x 2 2 - x 2
D2 + x 2 1 + x 2

Correct answer

A. 1 + x 2 2 + x 2

Step-by-step solution

Let c o t - 1 1 x = α ⇒ tan ⁡ α = x So, cos ⁡ α = 1 1 + x 2 ∴ sin ⁡ cot - 1 ⁡ cos ⁡ tan - 1 ⁡ x = s i n c o t - 1 1 1 + x 2 Let c o t - 1 1 1 + x 2 = β ⇒ cot ⁡ β = 1 1 + x 2 ∴ sin ⁡ β = ( 1 + x 2 ) ( 2 + x 2 ) ∴ sin ⁡ β = sin ⁡ c o t - 1 cos ⁡ cot - 1 ⁡ 1 x = 1 + x 2 2 + x 2

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