Home
Class 12
MATHS
If f(theta) = sin(tan^(-1)(sintheta/sqrt...

If `f(theta) = sin(tan^(-1)(sintheta/sqrt(cos2theta)))`, where `-pi/4 lt theta lt pi/4,` then the value of `d/(d(tantheta))\ f(theta)` is

Text Solution

Verified by Experts

`f(theta)=sin (tan^(-1)((sin theta)/(sqrt(cos 2theta))))," where "theta in (-(pi)/(4),(pi)/(4))`
`=sin (tan^(-1)((sin theta)/(sqrt(2 cos^(2) theta-1))))=sin (sin^(-1)(tan theta))=tan theta`
`therefore" "(d(tan theta))/(d(tan theta))=1`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Matrix Match Type|1 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Let f(theta)=sin(tan^(-1)((sin theta)/(sqrt(cos2 theta)))), wher e-(pi)/(4)

If f(theta)=sin(tan^(-1)((sin theta)/(sqrt(cos2 theta)))), where -(pi)/(4)

If sec theta=2cos theta , where (pi/2) lt theta lt pi , then what is the value of theta ?

If sin theta =sqrt(3) cos theta, -pi lt theta lt 0 , then the value of theta is

If tan8 theta = cot 2 theta , where 0 lt 8 theta lt pi/2 , then what is the value of tan 5 theta ?

If pi lt theta lt (3pi)/(2) , then find the value of sqrt((1-cos2theta)/(1+cos 2 theta)) .

If 3tantheta+4=0 where (pi)/(2)lt thetaltpi , then the value of 2cot theta-5costheta-sintheta .

sqrt(2+sqrt(2+2cos 4 theta)), forall 0 lt theta lt pi//4 is