Question

sin(cos^-1 x)

how to solve?

Answer 1

Answer:

$sin(cos^{-1}x)=\sqrt{1-x^2}$

Step-by-step explanation:

let us assume

$cos^{-1} x=\theta\\x=cos\theta$

now

$sin(cos^{-1}x)$ can be written as $sin\theta$

we know  $sin^2\theta+cos^2\theta=1$

so $sin^2\theta=1-cos^2\theta$

$sin\theta=\sqrt{1-cos^2\theta}$

now from above equation we can say that

$sin\theta=\sqrt{1-x^2}$

$sin(cos^{-1}x)=\sqrt{1-x^2}$