Prove that: 4\ costhetacos\ (pi/3+theta)...

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

Text Solution

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`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`

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Knowledge Check

The sum of all the solution of the equation cos theta cos ( pi/3 + theta) cos (pi/3 - theta) = 1/4, theta in [0, 6pi] is

A

`15 pi`

B

`30 pi`

C

`(100 pi)/3`

D

none

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