Home
Class 12
MATHS
If tan^(-1)x = theta, find the value of...

If `tan^(-1)x = theta`, find the value of `sin^(-1).(2x)/(1+x^(2))`

Text Solution

Verified by Experts

`tan^(-1) x = theta`
`rArr" "x tan = theta`
Now `sin ^(-1).(2x)/(1+x^(2)) = sin ^(-1) .(2tan theta)/(1+ tan^(2)theta)`
`" "= sin ^(-1)(sin 2theta)`
`" " = 2theta`
Promotional Banner

Topper's Solved these Questions

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Exericse 2a|30 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Exericse 2b|10 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|44 Videos

  • LINEAR PROGRAMMING

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|9 Videos

Similar Questions

Explore conceptually related problems

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

If 5x=sec theta and (5)/(x)=tan theta, find the value of 5(x^(2)-(1)/(x^(2)))

If (x -1) (x^(2) + 1) gt 0 , then find the value of sin((1)/(2) tan^(-1).(2x)/(1 - x^(2)) - tan^(-1) x)

If x in (0, 1) , then find the value of tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))

If x=tan15^(@) , then find the value of x^(2)+(1)/(x^(2)) .

If x >1 , then write the value of sin^(-1)((2x)/(1+x^2)) in terms of tan^(-1)x

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]

If x in [1, 0) , then find the value of cos^(-1) (2x^(2) - 1) - 2 sin^(-1) x

If x in [-1, 0) then find the value of cos^(-1) (2x^(2) -1) -2 sin^(-1) x

If x in[-1,0], then find the value of cos^(-1)(2x^(2)-1)-2sin^(-1)x