Find common roots of the equations `2sin^2x+sin^2 2x=2a n dsin2x+cos2x=tanxdot`

The number of distinct real roots of the equation sin^(3)x +sin^(2)x sin x-sin x- sin 2x-2cos x=0 belonging to the interval (-(pi)/(2),(pi)/(2))

Solve the equation sin^4x+cos^4x-2sin^2x+(3sin^2 2x)/4=0

Solve sin^2 2x - 2cos^2 x =0

Number of solutions of equation 2"sin" x/2 cos^(2) x-2 "sin" x/2 sin^(2) x=cos^(2) x-sin^(2) x for x in [0, 4pi] is

Suppose that for some angles xa n dy , the equations sin^2x+cos^2y=(3a)/2a n dcos^2x+sin^2y=(a^2)/2 hold simultaneously. the possible value of a is ___________

The number of distinct solutions of the equation 5/4cos^(2)2x + cos^4 x + sin^4 x+cos^6x+sin^6 x =2 in the interval [0,2pi] is

Number of solutions of the equation sin x + cos x-2sqrt(2) sin x cos x=0 for x in [0, pi] is

Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x )

Find the imtegrals of the functions (cos2x+2sin^(2)x)/(cos^(2)x)