Simplify :
`Sin^2( x^2 ) - Cos^2(x^2 )`

Simplify: (sin^(6)x+cos^(6)x)/(sin^(2)x cos^(2)x)

Simplify: ^(*)sin^(^^)(-1)((sin x+cos x)/(sqrt(2))),backslash-pi/4

Simplify tan^(-1)((cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2)))

int (sin ^ (2) x cos ^ (2) x) / ((sin ^ (5) x + cos ^ (3) x sin ^ (2) x + sin ^ (3) x cos ^ (2) x + cos ^ (5) x) ^ (2)) dx

((1) / ((sec x) ^ (2) - (cos x) ^ (2)) + (1) / ((cos ecx) ^ (2) - (sin x) ^ (2))) ( cos x) ^ (2) (sin x) ^ (2) = (1- (cos x) ^ (2) (sin x) ^ (2)) / (2+ (cos x) ^ (2) (sin x) ^ (2))

If f(x)=|[cos(x +x^2), sin(x +x^2),-cos(x+x^2)],[ sin(x-x^2), cos(x -x^2), sin(x-x^2)],[sin2x,0,sin2x^2]| then find f'(x)

Number of solutions of equation 2"sin" x/2 cos^(2) x-2 "sin" x/2 sin^(2) x=cos^(2) x-sin^(2) x for x in [0, 4pi] is

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx