The value of `intsqrt(1+secx)dx` is equal to (A) `2sin^-1(sqrt(2)sin(x/2))+c` (B) `2cos^-1(sqrt(2)sin(x/2))+c` (C) `2sin^-1(sqrt(2)cos(x/2))+c` (D) none of these

The value of intsqrt((sinx-sin^3x)/(1-sin^3x))dx is equal to (A) sin^-1sin^(3/2)x+C (B) 2/3sin^-1(sin^(3/2)x)+C (C) -2/3cos^-1(sin^(3/2)x)+C (D) none of these

The value of sin^-1 (sqrt(3)/2)+ sin^-1 (1/sqrt(2)) is equal to (A) sin^-1 ((sqrt(3+1))/(2sqrt(2))) (B) pi-sin^-1 ((sqrt(3+1))/(2sqrt(2))) (C) pi+sin^-1 ((sqrt(3+1))/(2sqrt(2))) (D) none of these

intsqrt(1+cos e cx)dx e q u a l s 2sin^(-1)sqrt(sinx)+c (b) sqrt(2)cos^(-1)sqrt(cosx)+c c-2sin^(-1)(1-2sinx) cos^(-1)(1-2sinx)+c

intsqrt((cosx-cos^3x)/(1-cos^3x))dx is equal to (a) -2/3sin^(-1)(cos^(3/2)x)+C (b) 3/2sin^(-1)(cos^(3/2)x)+C (c) 2/3cos^(-1)(cos^(3/2)x)+C (d) none of these

cos^(- 1)x=2sin^(- 1)sqrt((1-x)/2)=2cos^(- 1)sqrt((1+x)/2)

The value of int(sinx+cosx)/(sqrt(1-sin2x))\ dx is equal to (a) sqrt(sin2x)+C (b) sqrt(cos2x)+C (c) +-(sinx-cosx)+C (d) +-log(sinx-cosx)+C

intsqrt(x/(1-x))\ dx is equal to (a) sin^(-1)sqrt(x)+C (b) sin^(-1){sqrt(x)-sqrt(x(1-x))}+C (c) sin^(-1){sqrt(x(1-x))}+C (d) sin^(-1)sqrt(x)-sqrt(x(1-x))+C

sin^-1 (cos(sin^-1(sqrt(3)/2))= (A) pi/3 (B) pi/6 (C) - pi/6 (D) none of these

sqrt(3)int_0^pi dx/(1+2sin^2x)= (A) -pi (B) 0 (C) pi (D) none of these

If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sqrt(1+x^2)) -cos^(-1)1/(sqrt(1+x^2)) (d) -cos e c^(-1)(sqrt(1+x^2))/x