((cos x)/(1-sin x))*-(-3 pi)/(2)

Prove that ((sin ^ (3) x) / (1 + cos x) + (cos ^ (3) x) / (1-sin x)) = sqrt (2) sin ((pi) / (4) + x)

(sin (pi + x) cos ((pi) / (2) + x) tan ((3 pi) / (2) -x) cot (2 pi-x)) / (sin (2 pi-x) cos (2 pi + x) csc (-x) sin ((3 pi) / (2) -x)) = 1

If the expression cos(x-3(pi)/(2))+sin(3(pi)/(2)+x)+sin(32 pi+x)-18cos(19 pi-x)+cos(56 pi+x)-sin(x+17 pi) is expressed in the form of a sin x+b cos x, then a+b is equal to

If 0

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))=

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

If x in [0,2pi]" then "y_(1)=(sin x)/(|sin x|), y_(2)=(|cos x|)/(cos x) are identical functions for x in : I. (0,pi/2)" "II. (pi/2, pi)," "III. (pi,(3pi)/(2))," "IV. ((3pi)/(2),2pi)

If x in [0,2pi]" then "y_(1)=(sin x)/(|sin x|), y_(2)=(|cos x|)/(cos x) are identical functions for x in : I. (0,pi/2)" "II. (pi/2, pi)," "III. (pi,(3pi)/(2))," "IV. ((3pi)/(2),2pi)

Prove that int_(0)^((pi)/(2))(sin^(2)x)/(1+sin x cos x)dx=(pi)/(3sqrt(3))