(5.1sin^(3)x)/(pi^(2))*cos^(3)x

If f_(n)(x) = (sin x)/(cos3x)+(sin 3x)/(cos 3^(2)x) +(sin 3^(2)x)/(cos 3^(3)x) +....+ (sin 3^(n-1)x)/(cos 3^(n)x)"Then" f_(2) ((pi)/(4)) + f_(3) ((pi)/(4))=

The number of solution of the equation sin^(3)x cos x+sin^(2)x cos^(2)x+cos^(3)x sin x+1=0 in the interval [0, 2pi] is equal to

The number of solution of the equation sin^(3)x cos x+sin^(2)x cos^(2)x+cos^(3)x sin x=1 in the interval [0, 2pi] is equal to

The expression (tan(x-(pi)/(2))cos((3 pi)/(2)+x)-sin^(3)((7 pi)/(2)-x))/(cos(x-(pi)/(2))tan((3 pi)/(2)+x)) is equal to

(i) int_0^(pi//2) (sin^3x)/(sin^3x+cos^3x) dx (ii) int_0^(pi//2) (cos^3x)/(sin^3x+cos^3x) dx (iii) int_0^(pi//2) (sin^4x)/(sin^4x+cos^4x) dx (iv) int_0^(pi//2) (cos^5x)/(sin^5x+cos^5x) dx (v) int_0^(pi//2) (sin^5x)/(sin^5x+cos^5x) dx

The value of x satisfying the equation (sin^(-1)x)^(3)-(cos^(-1)x)^(3)+(sin^(-1)x)(cos^(-1)x)(sin^(-1)x-cos^(-1)x)=(pi^(3))/(16) is :

Prove that: (a) (cos(pi+x) cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^(2)x (b) cos((3pi)/2 + x)cos(2pi+x){cot ((3pi)/2-x)+cot(2pi+x)}=1

The expression (tan(x-(pi)/(2)).cos((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x)) simplifies to