The value of sin ⁡ cot

Let, cot − 1 x = A , cot 2 ⁡ A = x 2 1 + cot 2 ⁡ A = 1 + x 2 = c o s e c 2 A 1 sin 2 A = 1 + x 2 ⇒ sin A = 1 / 1 + x 2 ⇒ sin cot -1 x = 1 / 1 + x 2

Question: Answered & Verified by Expert

The value of

\sin (\cot^{- 1} x)

MathematicsInverse Trigonometric FunctionsJEE Main

Options:

Solution:

1181 Upvotes Verified Answer

The correct answer is:

\frac{1}{\sqrt{1 + x^{2}}}

Let,

\cot^{- 1} x = A, (\cot^{2} A) = x^{2}

1 + (\cot^{2} A) = 1 + x^{2} = c o s e c^{2} A

\frac{1}{{sin}^{2} A} = 1 + x^{2} \Rightarrow sin A = 1 / \sqrt{1 + x^{2}}

\Rightarrow sin ({cot}^{-1} x) = 1 / \sqrt{1 + x^{2}}

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