Integrating Square Roots

Question

Evaluate the integral:

_{0 ∫} ^2pi √((1-cosx)/2) dx

Answer 1

Think of making use of the following trigonometric identity:

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

Answer 2

Step 1: Rewrite cosx = 1-2sin^2(x/2)

Step 2: you can cancel 1's; 1-cosx = 2sin^2(x/2)

Step 3: now cancel the 2's, you will be left with sin(x/2)

Step 4: final step is to integrate sin(x/2) w.r.t dx