(cos x-sin x)/(1+sin2x)

Find the integral (cos x-sin x)/(1+sin 2 x)

int (cos x - sin x)/(1 + sin 2x) dx

Evaluate the following integrals : int (cos x + sin x )/(cos x - sin x ) (1- sin 2x) dx

(i) int (cos x-sin x)/sqrt(1+ sin 2x) dx (ii) int (cos x) /((cos (x/2)+sin (x/2))) dx

int (cos x - sin x)/ (1+2 sin x cos x ) dx is equal to a) - 1/(cos x- sin x)+c b) (cos x + sin x)/(cos x- sin x)+c c) - 1/(cos x+ sin x)+c d) x_1/(sin x+ cos x)+c

if a=(1+sin x)/(1-cos x+sin x) then (1+cos x+sin x)/(2sin x) is

(d)/(dx)[(1+cos2x+sin2x)/(1+sin2x-cos2x)]=

int _(0) ^(pi//2) (cos x dx )/((1+ sin x ) (2 + sin x ))

If A = {:[(1,tanx),(-tanx,1)] , show that : A'A^-1={:[(cos2x,-sin2x),(sin2x,cos2x)]

If A=[(1,tanx),(-tanx,1)] , Show that, A^TA^-1=[(cos2x,-sin2x),(sin2x,cos2x)] .