Question

prove that sina.cos2a = 1/4 sin4a.sec a

Answer 1

We can write 1/4 sin(4a)sec(a) as:

1/4 sin(4a)sec(a)=1/4*2sin(2a)*cos(2a)*1/(cos(a))=1/2*2sin(a)*cos(a)*cos(2a)*1/(cos(a))=sin(a)*cos(2a).


Here we use the next formulas: sin(2a)=2*sin(a)*cos(a);
sec(a)=1/(cos(a)).