(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))))

If cos ((x) / (2)) cos ((x) / (2 ^ (2))) cos ((x) / (2 ^ (3))) ...... oo = (sin x ) / (x) (1) / (2) tan ((x) / (2)) + (1) / (2 ^ (2)) tan ((x) / (2 ^ (2))) + ( 1) / (2 ^ (3)) tan ((x) / (2 ^ (3))) ... oo

lim_(x rarr sqrt(pi))(sin x^(2)-cos((3x^(2))/(2)))/(cos((x^(2))/(2))-sin(2x^(2))cos^(2)(x^(2))) is equal

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]]

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

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

Discuss the continuity of the function at x= 0 if f(x) = {:((e^(x^2) - cos x)/ x^2, x!=0),(3/2, x=0):}