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

If a sin x+b cos(x+theta)+b cos(x-theta)=d then the minimum value of |cos theta| is equal to (a) (1)/(2|b|)sqrt(d^(2)-a^(2))( b )(1)/(2|a|)sqrt(d^(2)-a^(2))(c)(1)/(2|d|)sqrt(d^(2)-a^(2))(d) none of these

Solution set of inequation ( cos^-1x)^2-(sin^-1x)^2gt0 is (A) [0, 1/sqrt(2)) (B) [-1, 1/sqrt(2)) (C) (-1,sqrt2) (D) none of these

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

The value of int(sin x+cos x)/(sqrt(1-sin2x))dx is equal to sqrt(sin2x)+C(b)sqrt(cos2x)+C(c)+-sin x-cos x)+C(d)+-log(sin x-cos x)+C

If sin^(-1)x-cos^(-1)x=pi/6 , then x= 1/2 (b) (sqrt(3))/2 (c) -1/2 (d) none of these

d/(dx)(sin^(-1)x+cos^(-1)x) is equal to : (A) (1)/(sqrt(1-x^(2))), (B) (2)/(sqrt(1-x^(2))), (C) 0 (D) sqrt(1-x^(2))

(d)/(dx)(cos (x/2))= (A) (1)/(2)sin(x)/(2) , (B) -(1)/(2)cos(x)/(2) (C) -(1)/(2)sin(x)/(2) , (D) -sin(x)/(4)

The value of sin^(-1)(cot(sin^(-1)((2-sqrt(3))/(4)+(cos^(-1)(sqrt(12)))/(4)+sec^(-1)sqrt(2))))(a)0( b) (pi)/(2)( c) (pi)/(3)( d) none of these

int sqrt((x)/(1-x))dx is equal to 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