" 4."sin x sin(cos x)

Examples: int_(0)^((pi)/(4))(sin x)/(sin x+cos x)dx

Prove that: sin" "3x" "+" "sin" "2x" "+" "sin" "x" "=" " 4" "sin" "x" "cos x/2 cos (3x)/2

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.

(cos 4x sin 3x -cos 2x sin x )/(sin 4x sin x+ cos 6x cos x)= tan 2x

Prove the following Identities (cos 4x sin 3x - cos 2xsin x)/(sin 4x.sin x +cos 6x.cos x)= tan 2x

Prove that (cos3x)/(sin2x sin4x)+(cos5x)/(sin4x sin6x)+(cos7x)/(sin6x sin8x)+(cos9x)/(sin8x sin10x)=(1)/(2)(cos ecx)[cos ec2x-cos ec10x]

Prove that: cosec xdotcosec2xdot sin4xdotcos6xdotcos e c 10 x=(cos3x)/(sin2x\ sin4x)+(cos5x)/(sin4x\ sin6x)+(cos7x)/(sin6x\ sin8x)+(cos9x)/(sin8x\ sin10 x)

show that (1)/(2sin x)(csc2x-cos ec4x)=(cos3x)/(sin2x sin4x) and hence prove that (cos3x)/(sin2x sin4x)+(cos5x)/(sin4x sin6x)+(cos7x)/(sin6x sin8x)+......+ terms =(1)/(2sin x)[cos ec2x-cos ec(2n+2)x]

int (9 cos x - sin x)/(4 sin x +5 cos x)dx

Evaluate int (9cos x-sin x)/(4sin x+5cos x) dx