Question

Sin(cos^-1 x)

how to solve?

Answer 1

`sin(cos^(-1)x)=√(1-x^2)`

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=√(1-cos^2\theta)`

now from above equation we can say that

`sin\theta=√(1-x^2)`

`sin(cos^(-1)x)=√(1-x^2)`