Question

prove:2cos ​2 x/2 = 1 + cos x

Answer 1

we know cos(A+B)=cosA.cosB-sinA
sinB
use this
cos (x/2+x/2)=cosx /2.cosx/2-sinx/2.sinx/2

cosx=cos^2 x/2-sin^2 x/2

cosx=cos^2 x/2-(1-cos^2 x/2)

cosx =2cos^2 x/2-1

cosx+1=2cos^2 x/2