Solve `sin 3alpha=4 sin alpha sin (x+alpha)sin(x-alpha)` where `alpha=n pi,n in Z`.

Prove that sin alpha+sin(alpha+2pi/3)+sin(alpha+4pi/3)=0

If A =[(cos alpha, sin alpha),(-sin alpha, cos alpha)] , then find A^(T) A.

If A=[(0, -tan""(alpha)/(2)),(tan""(alpha)/(2),0)] , then show that (I+A) =(I-A) [(cos alpha, - sin alpha),(sin alpha, cos alpha)] , where I is the identity matrix of order 2.

Find cot alpha . .

Find cot alpha . .

Find cot^2 alpha- cos^2 alpha . .

If A=[(cos alpha,sinalpha),(-sinalpha,cosalpha)] , prove by induction that A^n=[(cosnalpha,sinnalpha),(-sinnalpha,cosnalpha)],n in N

If sqrt2sin (60^@ -alpha)= 1 , then alpha is :

Prove that the locus of the points of intersection of the lines x cos alpha + y sin alpha = a and x sin alpha - y cos albha = b is a cicle, whatever may be alpha

If cos9alpha=sinalpha and 9alpha<90^@ then the value of tan 5alpha is