If alpha is a root of equation (1) and beta is a root of (2), ten `tanalpha+tanbetas `may be equal to (A) `1+sqrt(69)/6` (B) `1+2sqrt(69)/6` (C) `(3+sqrt(69))/6` (D) (-3-sqrt(69))/3`

Let alpha be a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a root of the equation 3cos^2x-10cosx+3=0 gamma be a root of the equation 1-sin2x=cosx-sinx 0<=alpha,beta,gamma<=pi/2 sin alpha+sin beta+sin gamma can be equal to (A) (14+3sqrt(2))/6 (B) 43226 (C) (3+4sqrt(2))/6 (D) (1+sqrt(2))/2

The value of sin(sin^-1 (1/2)+ cos ^-1 (1/3)) is equal to (A) (sqrt(3)+sqrt(8)/6 (B) (1+2sqrt(6))/6 (C) - (1+2sqrt(6))/6 (D) 0

Let alpha be a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a root of the equation 3cos^2x-10cosx+3=0 gamma be a root of the equation 1-sin2x=cosx-sinx 0<=alpha,beta,gamma<=pi/2 The value of sin (alpha-beta) is equal to (A) 1 (B) 0 (C) (1-2sqrt(6))/6 (D) (sqrt(3)-2sqrt(2))/6

Let alpha be a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a root of the equation 3cos^2x-10cosx+3=0 gamma be a root of the equation 1-sin2x=cosx-sinx 0<=alpha,beta,gamma<=pi/2 cos alpha+cos beta+cos gamma can be equal to (A) 3sqrt(6)+2sqrt(2)+6sqrt(2) (B) (3sqrt(3)+8)/12 (C) (3sqrt(3)+2)/6 (D) none of these

The value of sin(sin^-1 (1/2)+ cos ^-1 (1/3)) is equal to (A) ((sqrt(3)+sqrt(8))/6) (B) ((1+2sqrt(6))/6) (C) - ((1+2sqrt(6))/6) (D) 0

If alpha,beta are the roots of equation x^(2)-(2sqrt(3)+3i)x+6sqrt(3)i=0 and | alpha|>| beta| write value of (sqrt(3)alpha)/(2 beta)

(sqrt(-2))(sqrt(-3)) is equal to A. sqrt(6) B. -sqrt(6) C. isqrt(6) D. none of these

If tan^(-1)2x+tan^(-1)3x=(pi)/(2) , then the value of x is equal to a) (1)/(sqrt(6)) b) (1)/(6) c) (1)/(sqrt(3)) d) (1)/(sqrt(2))

root(3)(1+sqrt(2)).root(6)(3-2sqrt2)= ?

sqrt((4)/(3))-sqrt((3)/(4))=?(4sqrt(3))/(6) (b) (1)/(2sqrt(3))(c)1(d)-(1)/(2sqrt(3))