prove that ... integrate sqrt [(1-x)/(1+x)] dx ( upper limit = 1 , lower limit =0 ) = pi/2 - 1
by using x = cos 2 theta
thanks in advanced!
Note:
1. $\displaystyle \frac{1 - \cos (2 \theta)}{1 + \cos (2 \theta)} = \frac{1 - \cos^2 \theta + \sin^2 \theta}{1 + \cos^2 \theta - \sin^2 \theta} = \frac{2 \sin^2 \theta}{2 \cos^2 \theta} = \tan^2 \theta$.
2. $\displaystyle dx = -2 \sin (2 \theta) \, d \theta = -4 \sin \theta \cos \theta \, d \theta$.