[ Question 1.int(dx)/(sin x-cos x+sqrt(2)) equals [ (1) -(1)/(sqrt(2))tan((x)/(2)+(pi)/(8))+c, (an ((x)/(2)+(pi)/(8))+c (3) (1)/(sqrt(2))cot((x)/(2)+(pi)/(8))+c, (4) -(1)/(sqrt(2))cot((x)/(2)+(pi)/(8))+c]]

int(dx)/(cosx-sinx) is equal to a) (1)/(sqrt(2))log|tan(pi/2-pi/8)|+c b) (1)/(sqrt(2))log|cot(x/2)|+c c) (1)/(sqrt(2))log|tan(pi/2-(3pi)/(8))|+c d) (1)/(sqrt(2))log|tan(x/2+(3pi)/(8))|+c

int(dx)/(cosx+sqrt(3)sinx) equals: (1) 1/2logtan(x/2+pi/(12))+c (2) 1/2logtan(x/2-pi/(12))+c (3) logtan(x/2+pi/(12))+c (4) logtan(x/2-pi/(12))+c

int_(0)^( pi)|sin x|-|cos x||dx is equal to (a) tan((3 pi)/(8))( b) tan((pi)/(8))(c)4tan((pi)/(8))(d)2tan((3 pi)/(8))

int(1)/(sin x+sqrt(3)cos x)dx=(1)/(2)log tan((x)/(2)+(pi)/(3))+c

int_(0)^((pi)/(2))(dx)/(1+sqrt(tan x))=int_(0)^((pi)/(2))(dx)/(1+sqrt(cot x))=(pi)/(4)

intdx/(cosx-sinx) is equal to (A) 1/sqrt(2)log|tan(x/2-(3x)/8)|+C (B) 1/sqrt(2)log|cot(x/2)|+C (C) 1/sqrt(2)log|tan(x/2-pi/6)|+C (D) 1/sqrt(2)log|tan(x/2+(3pi)/8)|+C

int(1)/(sqrt(sin^(3)x cos x))dx is equal to :(A)-(2)/(sqrt(cos x))+c(B)(2)/(sqrt(tan x))+c(C)(2)/(sqrt(cot x))+c(D)(2)/(sqrt(tan x))+c

int(dx)/(sqrt(3)sin x+cos x)=A log_(e)tan(Bx+c)+K then (A)A=(1)/(2)(B)B=-(1)/(2)(C)C=(pi)/(12) (D) C=(pi)/(4)

If sin^(-1)x+sin^(-1)y=(pi)/(2) and sin2x=cos2y, then (a)x=(pi)/(8)+sqrt((1)/(2)-(pi^(2))/(64))(b)y=sqrt((1)/(2)-(pi^(2))/(64))-(pi)/(12)(c)x=(pi)/(12)+sqrt((1)/(2)-(pi^(2))/(64))(d)y=sqrt((1)/(2)-(pi^(2))/(64))-(pi)/(8)

lim_(x rarr1^(-))(sqrt(pi)-sqrt(2sin^(-1)x))/(sqrt(1-x))=(A)sqrt((2)/(pi))(B)sqrt((pi)/(2))(C)(1)/(pi)(D)sqrt((1)/(pi))