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

For x in (-pi, pi) find the value of x for which the given equation (sqrt 3 sin x + cos x)^(sqrt(sqrt3 sin 2 x-cos 2 x+2))=4 is satisfied.

For x in (-pi, pi) find the value of x for which the given equation (sqrt 3 sin x + cos x)^(sqrt(sqrt3 sin 2 x-cos 2 x+2))=4 is satisfied.

For x in (-pi, pi) find the value of x for which the given equation (sqrt 3 sin x + cos x)^(sqrt(sqrt3 sin 2 x-cos 2 x+2))=4 is satisfied.

For x in (-pi, pi) find the value of x for which the given equation (sqrt 3 sin x + cos x)^(sqrt(sqrt3 sin 2 x-cos 2 x+2))=4 is satisfied.

Solve (sin^(2) 2x+4 sin^(4) x-4 sin^(2) x cos^(2) x)/(4-sin^(2) 2x-4 sin^(2) x)=1/9 .

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

If sin x + sin ((pi)/(8) sqrt((1 - cos 2 x)^(2) + sin ^(2) 2 x)) = 0, x e [(5 pi)/(2), (7 pi)/(2)] , then x is

Solve cos ( sin^(-1)((x)/(sqrt(1+x^2))))= sin { cot^(-1) (3/4)}

Solve : sqrt(2cos^2x+1)+sqrt(2sin^2x+1)=2sqrt2