33*(2^(x)cos x)/((x^(2)+3)^(2))

(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

(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

Evaluate :lim_(n rarr oo)(cos((x)/(2))cos((x)/(2^(2)))cos((x)/(2^(3)))......cos((x)/(2^(n))))

sin x = 2 ^ (n) * cos (x) / (2) * cos (x) / (2 ^ (2)) * cos (x) / (2 ^ (3)) * ... * cos ( x) / (2 ^ (n)) * sin (x) / (2 ^ (n))

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

2cosx-cos3x-cos5x= ............... A) 16 cos ^(3) x sin ^(2) x B) 16 sin^(2) x cos ^(2) x C) 4 cos ^(2) x sin ^(2) x D) 4 sin ^(2) x cos ^(2)x

int(cos x)/([cos((x)/(2))+sin((x)/(2))]^(5))dx= 1) (2)/(3)[cosec((x)/(2))+sec((x)/(2))]^(3) 2) (2)/(3)[cos((x)/(2))+sin((x)/(2))]^(3)+C 3) (2)/(3)[sin((x)/(2))-cos((x)/(2))]^(3)+c 4) -(1)/(3)[sin((x)/(2))+cos((x)/(2))]^(-3)

int(cos x)/(cos((x)/(2))+sin((x)/(2)))^(5)dx=,[[" (A) "(2)/(3)(cosec((x)/(2))+sec((x)/(2)))^(3)+c," (B) "(2)/(3)(cos((x)/(2))+sin((x)/(2)))^(3)+c],[" (C) "(2)/(3)(sin((x)/(2))-cos((x)/(2)))^(-3)+c," (D) "-(2)/(3)(sin((x)/(2))+cos((x)/(2)))^(-3)+c]]

If x=sec57^(@) , then cot^(2)33^(@)+sin^(2)57^(@)+sin^(2)33^(@)+cosec^(2)57^(@)cos^(2)33^(@)+sec^(2)33^(@)sin^(2)57^(@) is equal to:

The extreme values of 4cos(x^(2)).cos((pi)/(3)+x^(2)).cos((pi)/(3)-x^(2)) are