(iv)cos(sin x^(2))

Integrate the functions (cos2x)/((cos x+sin x)^(2))

int(cos2x)/((cos x+sin x)^(2))dx

Find the derivative of cos( sin x^(2)) at x = sqrt(pi/2)

Find the derivative of cos( sin x^(2)) at x = sqrt(pi/2)

f_(1)(x)=sin^(-1)(cos(sin^(2)x)),f_(2)(x)=cos^(-1)(sin(cos^(2)x)),f_(3)(x)=sin^(-1)(cos^(2)x)),f_(4)(x)=cos^(-1)(sin^(2)x)* Then which of the following is/are correct?

int(dx)/(cos x(sin x+2))

Ltquad x rarr0 (1-cos ^ (2) (sin x) -cos (sin ^ (2) x) + cos ^ (2) (sin x) cos (sin ^ (2) x)) / (x ^ ( 6)) =

((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))

(cos x)/(sin^(2)x)

int (cos^(2)x+sin 2x)/((2 cos x- sin x)^(2))dx