Prove that: `\ s in3x+s in2x-s in x=4s in xcosx/2cos(3x)/2`

Prove that: s in3x+s in2x-s in x=4s in x(cos x)/(2)(cos(3x))/(2)

Prove that: s in3A+s in2A-s in A=4s in A(cos A)/(2)(cos A)/(2)cos3(A)/(2)(cos(3A))/(2)

Prove that: sin^(2)6x-sin^(2)4x=s in2xs in10x

Prove that: (s in5x-2s in3x+s in x)/(cos5x-cos x)=tan x

Prove that: cos^(2)2x-cos^(2)6x=s in4xs in8x

Prove that: (cos9x-cos5x)/(s in17x-s in3x)=-(s in2x)/(cos10x)

Prove that: s in x+s in3x++sin(2n-1)x=(sin^(2)nx)/(s in x) for all n in N.

The number of distinct real roots of the equation |cosx s in x s in x s in x cos x s in x s in x s in x cos x|=0 in the interval [-\ pi/4,pi/4] is- a. 3 b. \ 4 c. \ 2 d. 1

" Prove that " : int(2 sin x +3 cos x)/(3sin x+4 cos x) dx = (18x)/(25) +(1)/(25)log|3s sin x+ 4cosx|c

Evaluate: int(s in^6\ x+cos^6\ x)/(s in^2\ x\ cos^2\ x)