Home
Class 11
MATHS
In a triangleABC, prove that cos^2(2A)+c...

In a `triangleABC`, prove that `cos^2(2A)+cos^2(2B)+cos^2(2C)=1+2cos2Acos2Bcos2C`

Text Solution

Verified by Experts

We know, `A+B+C = pi`
`=>2A+2B+2C = 2pi`
`=>2A+2B = 2pi-2C`
`=>cos(2A+2B) = cos(2pi-2C)`
`=>cos(2A+2B) = cos2C`
`:.cos^2(2C) = cos^2(2A+2B) = [cos(2A+2B)]^2`
`cos^2 2C=[cos2Acos2B-sin2Asin2B]^2`
`cos^2 2C=[cos^2 2Acos^2 2B +sin^2 2Asin^2 2B-2sin2Asin2Bcos2Acos2B]`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If A+B+C=pi prove that cos^(2) A+cos^(2) B+cos^(2) C=1 - 2cos A cos B cos C .

Prove that (cos^(2)A-sin^(2)B)+1-cos^(2)C

If A+B+C=180^@ ,prove that cos^2A+cos^2B+cos^2C=1-2cos Acos B cos C .

If A, B, C are angles in a triangle , then prove that cos^(2)A+cos^(2)B-cos^(2)C=1-2sin Asin Bcos C.

If A+B+C=180, prove that cos^(2)A+cos^(2)B+cos^(2)C=1-2cos A cos B cos C

IF A,B,C are angles of a triangle , Prove that cos2A+cos 2B+cos 2C=-4cosAcosBcosC-1

If A+B+C=pi , prove that cos 2A +cos 2B +cos 2C=-1-4cos A cos Bcos C.

If A+B+C=pi , prove that cos 2A +cos 2B +cos 2C=-1-4cos A cos Bcos C.

If A+B+C=180^(@) then prove that cos^(2)A+cos^(2)B+cos^(2)C=1-2cosAcosBcosC