`cos^(2)sqrt(x)=cos^(2)x`

int(sin^(3)x)/((1+cos^(2)x)sqrt(1+cos^(2)x+cos^(4))x)dx is equal to

(i) int(2cos x)/(sqrt(1-4cos^(2) x))dx " "(ii) int (x+1)/(sqrt(x^(2)+1))dx

Find the real values of x for which the function f(x) = cos^(-1) sqrt(x^(2) + 3 x + 1) + cos^(-1) sqrt(x^(2) + 3x) is defined

Solve the inequality sin2x gtsqrt(2)sin^2x+(2-sqrt(2))cos^2x

Solve the inequality sin2x gtsqrt(2)sin^2x+(2-sqrt(2))cos^2x

The number of x in [0, 2pi] for which |sqrt(2"sin"^(4)x + 18"cos"^(2) x) -sqrt(2"cos"^(4)x + 18"sin"^(2)x)| = 1, is

Prove that sqrt(sin^4x+4cos^2x)-sqrt(cos^4x+4sin^2x)=cos2xdot

cos^(-1){1/2x^(2)+sqrt(1+x^(2))sqrt(1-x^(2))/(4)}=cos^(-1)(x)/(2)-cos^(-1)x

cos^(-1){1/2x^(2)+sqrt(1+x^(2))sqrt(1-x^(2))/(4)}=cos^(-1)(x/2)-cos^(-1)x

Find the general solution of the trigonometric equation sqrt(16cos^4x-8cos^2x+1)+sqrt(16cos^4x-24cos^2x+9)=2