" 15."(x sin x)/(1+cos^(2)x)

Find the extreme values of 11 cos^(2) x+ 15 sin x cos x- 9 sin^(2) x .

Integrate the following: int{(5cos^(3)x+2sin^(3)x)/(2sin^(2)x*cos^(2)x)+sqrt(1+sin2x)+(1+2sin x)/(cos^(2)x)+(1-cos2x)/(1+cos2x)}dx

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

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

[(Tan ( pi - x) Tan (1.5 pi + x))/(Cos^(2)(x-1.5pi))-(Cos(1.5pi + x))/(Sin(pi-x))]Sin^(2) (2pi-x)=

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?

Integrate the following: int{(5cos^3x+2sin^3 x)/(2sin^2 x*cos^2 x)+sqrt(1+sin2x)+(1+2sin x)/(cos^2x)+(1-cos2x)/(1+cos 2x)}dx

If f(x) = |(1+sin^(2)x,cos^(2)x,4 sin 2x),(sin^(2)x,1+cos^(2)x,4 sin 2x),(sin^(2)x,cos^(2)x,1+4 sin 2x)| What is the maximum value of f(x)?

(cos x)/(1-sin x)=(1+cos x+sin x)/(1+cos x-sin x)

{ cos (sin ^(-1) x)}^(2) ={sin (cos ^(-1) x)}^(2)