If ` 0 lt alpha,beta lt pi` `lim_(x rarr oo)(((sin alpha)^x +(sin beta)^x)/2)^(1/x) =1` then he value of `tan((alpha+beta)/3)` is

lim_(x rarr0)(sin alpha x)/(tan beta x)

lim_(x rarr00)(sin alpha x)/(sin beta x)=(alpha)/(beta)

If lim_(x rarr0)(x^(2)sin(beta x))/(alpha x-sin x)=1, when write the value of 18(alpha+2 beta)

let lim_(x rarr pi)(sin alpha x)/(1-2cos beta x)=-sqrt(3), then least positive value of alpha beta is

Let alpha,beta be such that pi lt alpha-beta lt3 pi . If sin alpha+ sin beta=(-21)/65 and cos alpha+ cos beta=(-27)/65 , then the value of cos((alpha-beta)/2) is

The value of lim_(x rarr0)(sin alpha x-sin beta x)/(e^(alpha x)-e^(beta x))

If 3sin alpha = sin beta!=0 , then the value of |(tan((alpha + beta)/2))/(tan((alpha-beta)/2))|

If sin alpha sin beta-cos alpha cos beta+1=0, then the value of 1+cot alpha tan beta is

If 0 lt alpha lt beta then lim_(n to oo) (beta^(n) + alpha^(n))^((1)/(n)) is equal to