Home
Class 11
MATHS
Prove that: 4\ costhetacos\ (pi/3+theta)...

Prove that: `4\ costhetacos\ (pi/3+theta)cos(pi/3-theta)=cos3theta`

Text Solution

Verified by Experts

`4 cos theta cos (frac{pi}{3}+theta) cos (frac{pi}{3}-pi)=cos 3 theta`

`arrow 4 cos theta cos (frac{pi}{3}+theta) cos (frac{pi}{3}-theta)`

`cos (A+B) cos (A-B) cos ^{2} A-cos ^{2} B`

`arrow 4 cos theta[cos ^{2} frac{pi}{3}-sin ^{2} theta]`

`arrow 4 cos theta[frac{1}{4}-1+cos ^{2} theta]`

`arrow-3 cos theta+4 cos ^{2} theta`

`arrow cos 3 theta`

Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINES

    RD SHARMA|Exercise Solved Examples And Exercises|488 Videos

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|120 Videos

Similar Questions

Explore conceptually related problems

Prove that (cos(pi+theta)cos(-theta))/(cos(pi-theta)cos((pi)/(2)+theta))=-cot theta

Prove that costhetacos""(theta)/(2)-cos3 thetacos""(9theta)/(2)=sin7thetasin8theta .

Prove that costhetacos((theta)/(2))-cos3thetacos((9theta)/(2))="sin"((7theta)/2)"sin"4theta

Prove that (cos^(3)theta-cos 3theta)/(cos theta)+("sin"^(3)theta+"sin" 3theta)/("sin" theta)=3 .

If theta=(pi)/(9), prove that cos theta cos2 theta cos3 theta cos4 theta=(1)/(16)

cos((3 pi)/(2)+theta)*cos(2 pi+theta)=

Prove that 4sin theta sin((pi)/(3)+theta)sin((2 pi)/(3)+theta)=sin3 theta

The sum of all the solution of the equation cos theta cos((pi)/(3)+theta)cos((pi)/(3)-theta)=(1)/(4)theta in[0,6 pi] (A) 15 pi(B)30 pi(C)(100 pi)/(3) (D) none of these

Prove that: cos^(2)theta+cos^(2)((pi)/(3)+theta)+cos^(2)((pi)/(3)-theta)=(3)/(2)