Evaluate sin `(pi + x) sin (pi - x) cosec^(2)x`

The value of sin(pi+x).sin(pi-x)."cosec"^(2)x is

Evaluate : cos^2 (pi/4 + x) - sin^2 (pi/4 -x)

Evaluate : sin^(2) (pi/8 +x/2) - sin^(2) (pi/8 - x/2)

Evaluate: int_0^(pi/2) (sin2x)/(sin^4x+cos^4x)dx

The least positive non integral solution of "sin" pi (x^(2) + x)-"sin" pi x^(2) = 0 , is

Evaluate : int_0^(pi/2)(sin^2x)/(sin x+cos x)dx

Find the solution of the equation ( sin x + cos x ) sin 2 x =a(sin^(3) x + cos^(3) x) located between (pi)/(2) and pi and for which values of 'a' does this equation have at most one solution satisfying the condition (pi)/(2) le x le pi .

Evaluate lim_(x to (pi)/(4)) ("sin" x - cos x)/(x - (pi)/(4))

Evaluate : int_(-pi/2) ^(pi/2) sin^2x dx

Evaluate: int(sin2x)/(sin(x-pi/3)sin(x+pi/3))\ dx