Home
Class 12
MATHS
Find value of Sin ( tan^(-1) x)...

Find value of ` Sin ( tan^(-1) x)`

Text Solution

Verified by Experts

Let `tan^-1x = theta`
Then, `x = tan theta`
`=>tan theta = x/1`
`:. sin theta = x/sqrt(x^2+1^2)`
`=>sin theta = x/sqrt(x^2+1)->(1)`
Now, `sin(tan^-1x ) = sin theta`
From (1),
`sin(tan^-1x ) = x/sqrt(x^2+1)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the value of Sin ( tan^(-1) x)

Find the value of int(tan sin^(-1)x)/(sqrt(1-x^(2)))dx

Find the value of : sin (sin ^(-1) ""(1)/(3) + sec ^(-1) 3)+cos( tan^(-1) ""(1)/(2) + tan ^(-1) 2)

if x greater than equal to 0 and less than equal to 1/2 then find the value of tan[sin^(-1){(x)/(sqrt(2))+sqrt((1-x^(2))/(2))}-sin^(-1)x]

Find the value of, cos [tan^(-1) {sin (cot^(-1)x)}]

Find the value of tan^(-1) ((cos x - sin x)/(cos x + sin x))

Find the value of : tan ^(-1) sin (-(pi)/(2))

Find the value of sin(cot^(-1)(tan(tan^(-1)x))),"x" in (0," 1]