If `y=(x^4-x^2+1)/(x^2+sqrt(3)x+1)a n d(dy)/(dx)=a x+b ,` then the value of a+b is (a)`cot(pi/8)` (b) `cot(pi/12)` (c) `tan((5pi)/12)` (d) `tan((5pi)/8)`

Find the value of tan^(-1) (-tan.(13pi)/(8)) + cot^(-1) (-cot((19pi)/(8)))

The value of cot((7pi)/16)+2cot((3pi)/8)+cot((15pi)/16) is (a) 4 (b) 2 (c) -2 (d) -4

The value of int_((-pi)/(2))^((pi)/(2))(x^(3)+xcosx+tan^(5)x+1)dx is

(sec2x-tan2x) equals a) tan(x-pi/4) b) tan(pi/4-x) c) cot(x-pi/4) d) tan^2(x+pi/4)

If cot^(-1) x = (2pi)/7 for some x in R the value of tan^(-1) x is :

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (a) (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (d) none of these

If cot^(-1)((n^2-10 n+21. 6)/pi)>pi/6, where x y<0 then the possible values of n is (a)3 (b) 2 (c) 4 (d) 8

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 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