The value of sin ( cot-1x) is

Question

The value of sin ( cot-1x) is (A) √1+x2 (B) x (C) (1+x2)-3/2 (D) (1+x2)-1/2

Tardigrade Admin · Accepted Answer

Put cot-1 x=A ∴ x=cot A <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/5149062dd2a54273918a953b8d1fdb95-.png" /> ∴ sin A = (1/√x2+1) = (1+x2)-1/2

Q. The value of $sin (cot^{- 1} x)$ is

$1 + x^{2}$

$x$

$(1 + x^{2})^{- 3/2}$

$(1 + x^{2})^{- 1/2}$

Put $co t^{- 1} x = A$
$∴ x = co t A$

$∴ s in A = \frac{1}{x ^{2} + 1} = (1 + x^{2})^{- 1 / 2}$

Q. The value of sin(cot−1x) is

1+x2​

x

(1+x2)−3/2

(1+x2)−1/2

Put cot−1x=A ∴x=cotA ∴sinA=x2+1​1​=(1+x2)−1/2

Q. The value of $sin (cot^{- 1} x)$ is

$1 + x^{2}$

$x$

$(1 + x^{2})^{- 3/2}$

$(1 + x^{2})^{- 1/2}$

Put $co t^{- 1} x = A$
$∴ x = co t A$

$∴ s in A = \frac{1}{x ^{2} + 1} = (1 + x^{2})^{- 1 / 2}$