Solve any one of the following `sin2x-sin4x+sin 6x=0`

Solve any one of the following cos x+sqrt(3) sin x=2

Prove any one of the following: (sin 5A-2sin 3A+sin A)/(cos 5A-cos A)=tan A

Solve any one of the following cos x+sin x=sqrt(2)

Prove any one of the following : sin^2A+sin^2B+sin^2C=2+2cos A cos Bcos C when A+B+C=pi .

Solve any one of the following sin theta+cos theta=sqrt 2

Solve any one of the following inequations and indicate the solution set on the real line. (4x+3)/(2x-x)<6

Prove any of the following: sin^2(pi/4)+sin^2(3pi/4)+sin^2(5pi/4)+sin^2(7pi/4)=2

Prove the following: sin^-1x-sin^-1y = sin^-1[x(sqrt(1-y^2))-y(sqrt(1-x^2))]