" (ii) "x sin x

Prove that: (i) sin 3x+"sin" 2x-"sin" x = 4 sin x cos((x)/(2))cos((3x)/(2)) (ii) ("sin" 3x+"sin" x)"sin" x+(cos 3x-cos x)cos x=0.

2tan2x = (cos x + sin x) / (cos x-sin x) - (cos x-sin x) / (cos x + sin x)

Prove that (cos x + sin x)/(cos x - sin x) - (cos x - sin x)/(cos x + sin x) = 2 tan x

if y = sin x ^ (sin x ^ (sin x))

The number of distinct real roots of the equation, |(cos x, sin x , sin x ),(sin x , cos x , sin x),(sinx , sin x , cos x )|=0 in the interval [-pi/4,pi/4] is :

x sin x (dy)/(dx) + (x cos x + sin x) = sin x

(cos 2x sin x + cos 6x sin 3x)/(sin 2x sin x + sin 6x sin 3x) =cot 5x

x sin x (dy) / (dx) + y (x cos x + sin x) = sin x