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

Let `f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta)))),w h e r e-pi/4

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|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Prove that sum_(r=1)^n(1/(costheta+"cos"(2r+1)theta))=(sinntheta)/(2sintheta* costheta*cos (n+1)theta),(w h e r e n in N)dot

(sintheta+sin2theta)/(1+costheta+cos2theta)

If 0 leq theta leq pi and sin(theta/2)=sqrt(1+sintheta)-sqrt(1-sintheta) ,then the possible value of tan theta , is -

(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?

(sin^3theta-cos^3theta)/(sintheta-costheta)-(costheta)/(sqrt(1+cot^2theta))-2tanthetacottheta=-1 if

Prove : (cos^2theta)/(1-tan theta) + (sin^3theta)/(sintheta - cos theta) = 1 + sin theta cos theta

A function f(theta)=sin^(2)theta+3sin theta cos theta+5cos^(2)theta is defined AA theta in R . Another function g(theta)=f((pi)/(2)-theta) at the point theta where f(theta) is minimum, then thevalue of (1)/(g(theta)) is

The value of 3(cos theta-sin theta)^(4)+6(sin theta+cos theta)^(2)+4 sin^(6) theta is where theta in ((pi)/(4),(pi)/(2)) (a) 13-4cos^(4) theta (b) 13-4cos^(6) theta (c) 13-4cos^(6) theta+ 2 sin^(4) theta cos^(2) theta (d) 13-4cos^(4) theta+ 2 sin^(4) theta cos^(2) theta

Given that f(ntheta)=(2sin2theta)/(cos2theta-cos4ntheta), and f(theta)+f(2theta)+f(3theta)++f(ntheta)=(sinlambdatheta)/(sinthetasinmutheta), then the value of mu-lambda is ______

IF sintheta=sqrt3/2 , then cos theta =?