Question

(cosA + cosB) square + sinA-sin B square=

Answer 1

first of all this is not history it is maths so your selection of subjects is only wrong..

Answer 2

Prove (cosA+cosB)^2+(sinA-sinB)^2 = 4cos^2(A+B)/2  (cosA+cosB)^2 + (sinA-sinB)^2  => (cos^2A + cos^2B + 2cosAcosB) + (sin^2A + sin^2B - 2sinAsinB)  => cos^2A + cos^2B + sin^2A + sin^2B + 2cosAcosB - 2sinAsinB  => cos^2A + sin^2A + cos^2B + sin^2B + 2(cosA*cosB - sinA*sinB)   => 1 + 1 + 2(cosA*cosB - sinA*sinB)   => 2 + 2(cosA*cosB - sinA*sinB)   => 2 (1 + (cosA*cosB + sinA*sinB))  => 2 * (1 + cos(A-B))   {Because: cosA*cosB - sinA*sinB = cos(A+B)}  => 2 * 2cos^2 ((A+B)/2)  => 4cos^2 (A+B)/2