`lim_(alpha rarr 0) (tan alpha- sin alpha)/alpha^3`

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

lim_(x rarr0)(sin(alpha+x)-sin(alpha-x))/(cos(alpha+x)-cos(alpha-x))

lim_(alpha to 0) (sin (alpha^n))/((sin alpha)^(m))

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

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

Let m and n be two positive integers greater than 1. If lim_(alpha rarr0)(e^(cos alpha^(n))-e)/(alpha^(m))=-((e)/(2)) then the value of (m)/(n) is

Prove the following identities: (sin alpha sin 11 alpha + sin 3 alpha sin 7 alpha)/(sin alpha cos 11 alpha + sin 3 alpha cos 7 alpha)= tan 8 alpha