What trigonometric identity is this

Question

1+costhetha= 2cos² (1⁄2thetha) 

Answer 1

cos(θ/2) = ±√[(1+cosθ)/2]  (half angle identity for cosine)

 

So, cos²(θ/2) = (1+cosθ)/2

 

Therefore, 2cos²(θ/2) = 2(1+cosθ)/2

 

                                = 1+cosθ