If `tan alpha=3 and tan beta=(1)/(2)`, then which of the following is true ?

Let alpha and beta be nonzero real numbers such that 2(cosbeta?cosalpha)+cosalpha cosbeta =1 . Then which of the following is/are true? (a) sqrt 3 tan(alpha/2)+tan(beta/2)=0 (b) sqrt3 tan(alpha/2)?tan(beta/2)=0 (c) tan(alpha/2)+sqrt3tan(beta/2)=0 (d) tan(alpha/2)?sqrt 3tan(beta/2)=0

Let alphaa n dbeta be nonzero real numbers such that 2(cosbeta-cosalpha)+cosalphacosbeta=1 . Then which of the following is/are true? sqrt(3)tan(alpha/2)+tan(beta/2)=0 sqrt(3)tan(alpha/2)-tan(beta/2)=0 t a n""(alpha/2)+sqrt(3)tan(beta/2)=0 t a n""(alpha/2)-sqrt(3)tan(beta/2)=0

If tan alpha=(1)/(3) and tan (beta)=(1)/(2) then tan (alpha+beta)=

If tan alpha = 1/3 and tan beta = 1/2 , then: tan(alpha + beta) =

If 2tan alpha=3tan beta then tan(alpha-beta)=

If tan alpha.tan beta=a and alpha+beta=(pi)/(3) then tan alpha and tan beta are the roots of the equation

If tan (alpha + beta) = 2 and tan (alpha - beta) = 1, then tan (2 alpha ) is equal to:

(1+tan alpha tan beta)^(2) + (tan alpha -tan beta)^(2) =

If" " n tan alpha = (n+1) tan beta " then show that", tan (alpha - beta) = (sin 2 beta)/(2n + 1 - cos2 beta).

(1+ tan alpha tan beta)^(2) + (tan beta - tan beta)^(2)=