The value of sin ((cot)- 1 ⁡ x) is

Question

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

Tardigrade Admin · Accepted Answer

Let, (cot)- 1 textx = textA , (cot)2 A = x2 1+(cot)2 A =1+x2=cosec2A (1/ textsin2 textA) = 1 + textx2 â textsin textA = 1 / √1 + textx2 ⇒ textsin ( textcot-1 textx) = 1 / √1 + ( textx)2

Q. The value of $s in ((co t)^{- 1} x)$ is

$1 + x^{2}$

$x$

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

$1 - x^{2}$

Let, $(co t)^{- 1} x = A, (co t)^{2} A = x^{2}$
$1 + (co t)^{2} A = 1 + x^{2} = cose c^{2} A$
$\frac{1}{sin ^{2} A} = 1 + x^{2} \Rightarrow sin A = 1/ 1 + x^{2}$
$\Rightarrow sin (cot^{- 1} x) = 1/ 1 + (x)^{2}$

Q. The value of sin((cot)−1⁡x) is

1+x2​

x

1+x2​1​

1−x2​

Let, (cot)−1x=A,(cot)2A=x2 1+(cot)2A=1+x2=cosec2A sin2A1​=1+x2⇒sin A=1/1+x2​ ⇒sin(cot−1x)=1/1+(x)2​

Q. The value of $s in ((co t)^{- 1} x)$ is

$1 + x^{2}$

$x$

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

$1 - x^{2}$

Let, $(co t)^{- 1} x = A, (co t)^{2} A = x^{2}$
$1 + (co t)^{2} A = 1 + x^{2} = cose c^{2} A$
$\frac{1}{sin ^{2} A} = 1 + x^{2} \Rightarrow sin A = 1/ 1 + x^{2}$
$\Rightarrow sin (cot^{- 1} x) = 1/ 1 + (x)^{2}$