Establish the identity cos alpha beta cos alpha beta 2 c

Establish the identity cos (alpha + beta) + cos (alpha - beta) = 2 cos alpha cos beta. Which of the following four statements establishes the identity? A. cos (alpha + beta) + cos (alpha - beta) = (sin alpha cos beta + cos alpha sin beta) + (sin alpha cos beta - cos alpha sin beta) = 2 cos alpha cos beta B. cos (alpha + beta) + cos (alpha - beta) = (sin alpha cos beta + cos alpha sin beta) - (sin alpha cos beta - cos alpha sin beta) = 2 cos alpha cos beta C. cos (alpha + beta) + cos (alpha - beta) = (cos alpha cos beta + sin alpha sin beta) - (cos alpha cos beta - sin alpha sin beta) = 2 cos alpha cos beta D. cos (alpha + beta) + cos (alpha - beta) = (cos alpha cos beta - sin alpha sin beta) + (cos alpha cos beta + sin alpha sin beta) = 2 cos alpha cos beta

Solution

we know cos(A+B) = cos A cos B sin A sin B

  cos(AB) = cos A cos B + sin A sin B

then

ans D

cos(a+b) + cos(a-b) = cosa cosb - sina sinb + cosa cosb + sina sinb

= 2cosa cosb