`f(x)=(sin x)/(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)`

(sin^3theta-cos^3theta)/(sintheta-costheta)-(costheta)/(sqrt(1+cot^2theta))-2tanthetacottheta=-1 if (a) theta in (0,pi/2)-{pi/4} (b) theta in (pi/2,pi) theta in (pi,(3pi)/2) (d) theta in ((3pi)/2,2pi)

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

cos 2x- 3 cos x + 1=(1)/((cot 2 x - cot x)sin (x-pi)) holds , if

If x=2cos^(-1)(1/2)+sin^(-1)(1/(sqrt(2)))+tan^(-1)(sqrt(3))\ a n d\ y=cos(1/2sin^(-1)(sin(x/2))) then which of the following statement holds good? a. y=cos((3pi)/16) b. y=cos((5pi)/16) c. x=4cos^(-1)y d. none of these

Find the values of the following :- (a)sin(2pi+(pi)/(6)),(b)cos(2pi+(pi)/(3))

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x