Question

prove that


sin A + sin 3 A + sin 5 A + sin
cos A + cos 3A + cos 5 A + cos 7A
=tan 4A.​

Answer 1

here we have to use the formulas of sinC+ sinD & cosC+cosD

Now,

(2 sin4A cos3A + 2 sin4A cosA)/(2 cos4A cos3A+ 2 cos4A cosA)

taking common 2 sin4A from numerator and 2 cos4A from denominator

= 2 sin4A/2 cos4A

= tan4A

hence proved