lim_(a rarr pi)(sin alpha)/(1-(alpha^(2))/(pi^(2)))

lim_(alpha rarr(pi)/(4))(sin alpha-cos alpha)/(alpha-(pi)/(4))

lim_(x rarr2)((cos alpha)^(x)+(sin alpha)^(x)-1)/(x-2)

If alpha,beta in(-(pi)/(2),0) such that (sin alpha+sin beta)+(sin alpha)/(sin beta)=0 and (sin alpha+sin beta)(sin alpha)/(sin beta)=-1 and lambda=lim_(n rarr oo)(1+(2sin alpha)^(2n))/((2sin beta)^(2n))

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

Prove that lim_(x rarr4)((cos alpha)^(x)-(sin alpha)^(x)-cos2 alpha)/(x-4)=cos^(4)alpha ln(cos alpha)-sin^(4)alpha,alpha in(0,(pi)/(2))

For alpha>0, let lim_(x rarr pi)(tan2x)/(x-pi)=lim_(x rarr0)((1-cos2 alpha x)^(2))/(x^(4)) then alpha is equal to

Obtain Lim_(xrarr2) ((Cos alpha)^(x)+(Sin alpha)^(x)-1)/(x-2) , where (0 lt alphalt pi/2)