If `pi/2 < theta < (3pi)/2` then `sqrt ((1-sin theta)/(1+sin theta))=` `a. sec theta-tan theta, b. sec theta + tan theta, c. tan theta-sec theta, d.` none of these

The argument of (1-i)/(1+i) is a. -pi/2 b. pi/2 c. (3pi)/2 d. (5pi)/2

Let f(x) =(kcosx)/(pi-2x) if x!=pi/2 and f(x)=3 if x=pi/2 then find the value of k if lim_(x->pi/2) f(x)=f(pi/2)

1.The inverse of cosine function is defined in the intervals (A) [ -pi , 0 ] (B) [ -pi/2,0 ] (C) [ 0,pi/2 ] (D) [ pi/2 , pi ]

int_0^(pi/2)sin4xcotx dx is equal to -pi/2 (2) 0 (3) pi/2 (4) pi

int_0^pi cos2xlogsinxdx= (A) pi (B) -pi/2 (C) pi/2 (D) none of these

The possible values of theta in (0,pi) such that sin (theta) + sin (4theta) + sin(7theta) = 0 are (1) (2pi)/9 , i/4 , (4pi)/9, pi/2, (3pi)/4 , (8pi)/9 (2) pi/4, (5pi)/12, pi/2 , (2pi)/3, (3pi)/4, (8pi)/9 (3) (2pi)/9, pi/4 , pi/2 , (2pi)/3 , (3pi)/4 , (35pi)/36 (4) (2pi)/9, pi/4, pi/2 , (2pi)/3 , (3pi)/4 , (8pi)/9

The possible values of theta in (0,pi) such that sin (theta) + sin (4theta) + sin(7theta) = 0 are (1) (2pi)/9 , i/4 , (4pi)/9, pi/2, (3pi)/4 , (8pi)/9 (2) pi/4, (5pi)/12, pi/2 , (2pi)/3, (3pi)/4, (8pi)/9 (3) (2pi)/9, pi/4 , pi/2 , (2pi)/3 , (3pi)/4 , (35pi)/36 (4) (2pi)/9, pi/4, pi/2 , (2pi)/3 , (3pi)/4 , (8pi)/9

lim_(x to pi/2) (tan2x)/(x-(pi)/(2))

f(x)=(s i nx)/(sqrt(1+tan^2x))+(cos x)/(sqrt(1+cot^2x)) is constant in which of following interval a. \ (0,\ pi/2) b. (pi/2,\ pi) c. (pi,\ (3pi)/2) d. ((3pi)/2,2pi)

The value of cos^(-1)(-1)-sin^(-1)(1) is: a. pi b. pi/2 c. (3pi)/2 d. -(3pi)/2