Question

If
P=Sin A.Sin B,
Q= Sin C.Cos A,
R = Sin A.Cos B and
S=Cos A.Cos C
then
5(P^2+Q^2+R^2+S^2) = ??

Answer 1

We can see that

 P^2 + R^2 =  {sin(A)}^2     and  Q^2 + S^2 = {Cos(A)}^2

adding we get P^2 + R^2 + Q^2 + S^2 = 1

So
5(P^2 + R^2 + Q^2 + S^2) = 5