Solve : `2sin(3x+pi/4)=sqrt(1+8sin2x*cos^2 2x)`

Solve sin x+sqrt(3)cos x=sqrt(2)

Over [-pi,pi] the solution of 2sin^(2)(x+(pi)/(4))+sqrt(3)cos2x>=0 is

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0

Solve 2 sin^(2) x-5 sin x cos x -8 cos^(2) x=-2 .

Solve sin x-3 sin 2x + sin 3x = cos x -3 cos 2x + cos 3x .

Solve sin^(2)x+(1)/(4)sin^(2)3x=sin x sin^(2)3x

Solve: sin^(-1)x + sin^(-1)2x = pi/3 .

Solve sin x("cos"x/4-2 sin x)+(1+"sin"x/4-2 cos x)cos x =0 .

Solve the equation 4^(sin2x+2cos^(2)x)+4^(1-sin2x+2sin^(2)x)=65

Solve 2sin^(2)x-5sin x cos x-8cos^(2)x=-2