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

lim_(alphato0)(sin(alpha^(n)))/((sinalpha)^(m))

Let m and n be two positive integers greater than 1.If lim_(alpha->0) (e^(cos alpha^n)-e)/(alpha^m)=-(e/2) then the value of m/n is

Let lambda and alpha be real. Then the numbers of intergral values lambda for which the system of linear equations lambdax +(sin alpha) y+ (cos alpha) z=0 x + (cos alpha) y+ (sin alpha) z=0 -x+(sin alpha) y -(cos alpha) z=0 has non-trivial solutions is

Prove that sin 4alpha = 4 tan alpha (1 - tan^(2) alpha)/((1 + tan^(2) alpha)^(2))

If y = (2 sin alpha )/(1 + cos alpha + sin alpha) then, prove that (1 - cos alpha + sin alpha)/(1 + sin alpha) = y .

sin 3 alpha = 4 sin alpha sin(x + alpha) sin(x-alpha)

If A=[(0,-tan alpha),(2,tan alpha),(2,0)] and I is 2 xx 2 unit matrix, then (I-A)[(cos alpha,sin alpha),(sin alpha, sin alpha)] is (a) -I+A (b) I-A (c) -I-A (d) non of these