Prove that (sin A + sin 3A + sin 5A + sin7 A)/(Cos A + Cos3 A + cos5 A + cos7 A) = tan 4A.

Question

Prove that \(\frac{sin\,A+sin3\,A+sin5\,A+sin7\,A}{cos\,A+cos3\,A+cos5\,a+cos7\,A}=tan\,4\,A.\)

Answer 1

LHS = \(\frac{(sin\,7A+sin\,A)+(sin\,5A+sin\,3A)}{(cos\,7A+cos\,A)(cos\,5A+cos\,3A)}\)