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Prove that cosalpha+cosbeta+cosgamma+cos...

Prove that `cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos((alpha+beta)/2)cos((beta+gamma)/2)cos((gamma+alpha)/2)`

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If alpha + beta + gamma = 2 theta , prove that cos theta + cos(theta- alpha) + cos(theta- beta) + cos(theta -gamma) = 4(cos (alpha/2) cos (beta/2) cos (gamma/2))

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