Prove that `(1+cos x)/(sin x)`=`(cos( x/2))/(sin (x/2))`

Prove that (cos 3 x)/(sin 2 xsin 4x)+(cos 5x)/(sin 4xsin 6x)+(cos 7x)/(sin 6xsin 8x)+(cos 9x)/(sin 8x sin 10x) =(1)/(2) (co sec x)[co sec2x-co sec 10x]

Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^2x

Prove that : cos (2 sin^(-1) x) = 1-2x^2

Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x)} =cot^2x

Prove that: (sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27 x)=(1/2)(tan27 x-tanx)

Prove that: (sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27 x)=(1/2)(tan27 x-tanx)

Prove that : (cos 4x sin 3x - cos 2x sin x)/(sin 4x .sin x + cos 6x .cos x) = tan 2x

Prove that : cos^(-1) x = 2 cos^(-1) sqrt((1+x)/(2)) (ii) Prove that : tan^(-1)((cosx + sin x)/(cosx - sin x)) = (pi)/(4)+ x

Prove that sinx/cos(3x)+sin(3x)/cos(9x)+sin(9x)/cos(27x)=1/2 (tan27x-tanx)

Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x) = (pi)/(2), |x| le 1