If `sinx+cosx=sqrt(y+1/y)` for `x in [0,pi]` , then (a) `x=pi/4` (b) `y=0` (c) `y=1` (d) `x=(3pi)/4`

If xa n dy are positive acute angles such that (x+y) and (x-y) satisfy the equation tan^2theta-4tantheta+1=0, then x=pi/6 (b) x=pi/4 (c) y=pi/6 (d) y=pi/4

One of the root equation cosx-x+1/2=0 lies in the interval (a) (0,pi/2) (b) (-pi/(2,0)) (c) (pi/2,pi) (d) (pi,(3pi)/2)

If (sinx)(cosy)=1/2, then (d^2y)/(dx^2) at (pi/4,pi/4) is (a) -4 (b) -2 (c) -6 (d) 0

If cosx=(2cosy-1)/(2-cosy), where x , y in (0,pi) then tan(x/2)cot(y/2) is equal to sqrt(2) (b) sqrt(3) (c) 1/(sqrt(2)) (d) 1/(sqrt(3))

The smallest positive value of x (in radians) satisfying the equation (log)_(cosx)((sqrt(3))/2sinx)=2-(log)_(secx)(tanx) is (a) pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

The sum of all the solution in [0,4pi] of the equation tanx+cotx+1=cos(x+pi/4)i s (a) 3pi (b) pi/2 (c) (7pi)/2 (d) 4pi

If lim_(x->0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0 ,where theta in (-pi,pi], then the value of theta is (a) +-pi/4 (b) +-pi/3 (c) +-pi/6 (d) +-pi/2

If (2+sinx)(dy)/(dx)+(y+1)cosx=0 and y(0)=1 , then y((pi)/(2)) is equal to

If x , y in [0,2pi]a n dsinx+siny=2, then the value of x+y is pi (b) pi/2 (c) 3pi (d) none of these

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in (-pi/2,pi/4) (b) (0,pi/2) (-pi/2,pi/2) (d) (pi/4,pi/2)