If A, B, C are the angles of a triangle, prove that cos^{2}A + cos^{2}B + cos^{2 }C = 1-2cosAcosBcosC

I've tried to use A+B+C=180, but I can't get the cos^{2 separately.. }

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- Jun 28th 2013, 07:54 PMTrefoil2727supplementary exercise of trigo
If A, B, C are the angles of a triangle, prove that cos

^{2}A + cos^{2}B + cos^{2 }C = 1-2cosAcosBcosC

I've tried to use A+B+C=180, but I can't get the cos^{2 separately.. } - Jun 28th 2013, 10:28 PMmpx86Re: supplementary exercise of trigo
this will help u

it is done for A+B=C

if A+B=C then prove that cos2A+cos2B + cos2C=1+2cosAcosB cos

it is ur task to do the same for a+b+c=180(method used will be identical) - Jun 29th 2013, 05:27 AMTrefoil2727Re: supplementary exercise of trigo
- Jun 29th 2013, 06:10 AMmpx86Re: supplementary exercise of trigo
½[sin ( Q+ β) + sin (Q − β)] = sin Q cos β,

so that

sin ( Q+ β) + sin ( Q− β) = 2 sin Q cos β. . . . . . (1)

Now put

Q + β = A

and

Q− β = B. . . . . . . . . . . . . . . .(2)

The left-hand side of line (1) then becomes

sin A + sin B.

This is now the left-hand side of (e), which is what we are trying to prove.

To complete the right−hand side of line (1), solve those simultaneous equations (2) for Q and β.

On adding them, 2Q = A + B,

so that

Q = ½(A + B).

On subtracting those two equations, 2β = A − B,

so that

β = ½(A − B).

On the right−hand side of line (1), substitute those expressions for and β. Line (1) then becomes

sin A + sin B = 2 sin ½(A + B) cos ½(A − B).

HERE A=2C AND B=2D

SUCH THAT sin 2C + sin 2D = 2 sin(C + D) cos (C − D).

IT IS YOUR TASK TO PROVE TH SAME FOR ADDITION OF 2 COSINES....