Find sum of all possible value of `theta` in the interval `(-(pi)/2,pi)` for which `(3+2isin theta)/(1-2sini theta)` is purely imaginary (a) `(pi)/(3)` (b) `(pi)` (c) `(2pi)/(3)` (d) `(pi)/(2)`

Find real theta varepsilon (-pi,pi) so that (3+2isintheta)/(1-2isintheta) is purely imaginary .

Let A={theta in (-pi /2,pi):(3+2i sin theta )/(1-2 isin theta ) is purely imaginary } Then the sum of the elements in A is

If (3+2i sintheta)/(1-2i sintheta) is a real number and 0lt theta lt 2pi , then theta is a. pi \ b. pi/2 \ c. pi/3 \ d. pi/6

The period of cos5 theta is (a) pi^(2) (b) 2 pi (c) 2 pi/5 (d) pi/3

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

If (1-tantheta)/(1+tantheta) = 1/sqrt3 , where theta in (0, pi/2) , then theta = (a) pi/6 (b) pi/4 (c) pi/12 (d) pi/3

int_(-(pi)/(2))^((pi)/(2))cos^(3)theta(1+sin theta)^(2)d theta is equal to

cos((3 pi)/(2)+theta)*cos(2 pi+theta)=

If pi

A value of theta satisfying cos theta+sqrt(3)s int h eta=2 is (5 pi)/(3) b.(4 pi)/(3) c.(2 pi)/(3) d.(pi)/(3)