The exhaustive set of value of a for which `a-cot^(-1)3x=2tan^(-1)3x+cos^1xsqrt(3)+sin^(-1)xsqrt(3)m a yh a v e` solution, is `[-pi/4,pi/4]` (b) `[pi/2,(3pi)/2]` `[(2pi)/3,(4pi)/3]` (d) `[-(3pi)/6,(7pi)/6]`

If y=tan^(-1)x+tan^(-1)(1/x)+sec^(-1)x , then y lies in the interval (a) [pi/2,pi)uu[pi,(3pi)/2) (b) [pi/2,(3pi)/2] (c)(0,pi) (d) [0,pi/2)uu[pi/2,pi)

The solution set of the equation 4s int h eta cos theta-2cos theta-2sqrt(3)s int_(h eta)+sqrt(3)=0 in the interval (0,2 pi) is {(3 pi)/(4),(7 pi)/(4)} (b) {(pi)/(3),(5 pi)/(3)}{(3 pi)/(4),pi,(pi)/(3)(5 pi)/(3)}(d){(pi)/(6),(5 pi)/(6),(11 pi)/(6)}

sin^(-1)((-1)/2) (a) pi/3 (b) -pi/3 (c) pi/6 (d) -pi/6

The value of cos^(-1)sqrt((2)/(3))-cos^(-1)((sqrt(6)+1)/(2sqrt(3))) is equal to (A)(pi)/(3)(B)(pi)/(4)(C)(pi)/(2)(D)(pi)/(6)])

The range of f(x)=sin^(-1)(sqrt(x^(2)+x+1)) is (0,(pi)/(2))(b)(0,(pi)/(3))(c)((pi)/(3),(pi)/(2)) (d) [(pi)/(6),(pi)/(3)]

cot^(-1)(-sqrt3)= (a) -pi/6 (b) (5pi)/6 (c) pi/3 (d) (2pi)/3

If 4cos^(2)theta=3 then theta =---- 1) (pi)/(6),(5 pi)/(6) 2) (pi)/(4),(3 pi)/(4) 3) (pi)/(3),(2 pi)/(3) 4) +-(pi)/(2)

Given both theta and phi are acute angles and sin theta=(1)/(2),cos varphi=(1)/(3), then the value of theta+varphi belongs to (a)((pi)/(3),(pi)/(2)]( b) ((pi)/(2),(2 pi)/(3)] (c) ((2 pi)/(3),(5 pi)/(6)] (d) ((5 pi)/(6),pi]

If tan^(-1)(x^(2)+3|x|-4)+cot^(-1)(4 pi+sin^(-1)sin14)=(pi)/(2), then the value of sin^(-1)sin2x is (a)6-2 pi( b) 2 pi-6( c) pi-3 (d) 3-pi

If sin^(-1)x+sin^(-1)y=(2 pi)/(3) ,then the value of cos^(-1)x+cos^(-1)y is (A) (2 pi)/(3) (B) (pi)/(3) (C) (pi)/(2) (D) pi