The equation `2 "cos"^(2)((x)/(2))"sin"^(2) x = x^(2) + (1)/(x^(2)), 0 le x le (pi)/(2)` has

Number of solutions of the equation cos^(4) 2x+2 sin^(2) 2x =17 (cos x + sin x)^(8), 0 lt x lt 2 pi is

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 .

Solve the differential equation cos^(2) x ( dy)/( dx) + y = tan x ( 0 le x lt (x)/(2) ) .

Number of solutions of the equation sin^(4) x-cos^(2)x sin x + 2 sin^(2) x+sin x=0 in 0 le x le 3pi is ________.

Prove that cos^-1 ((sin x + cos x )/(sqrt2)) = x - (pi/4), (pi/4) le x le ((5pi)/4)

Solve the following equations. cos^-1((1-x^2)/(1+x^2)) + tan^-1 ((2x)/(1-x^2)) = (2pi)/3, 0 le x < 1

The number of real solution of the equation sqrt(1 + cos 2x) = sqrt2 sin^(-1) (sin x), -pi le x le pi , is