Answer:
see explanation
Step-by-step explanation:
Using the sum to product identity
cosx + cosy = 2cos( )cos( )
Consider left side
(cos5A +cos3A) + (cos15A + cos7A)
= 2cos( )cos( ) + 2cos( ) cos( )
= 2cos() cos() + 2cos( )cos( )
= 2cos4AcosA + 2cos11A cos4A ← factor out 2cos4A from both terms
= 2cos4A( cos11A + cosA) ← repeat the process
= 2cos4A( 2cos( )cos( )
= 2cos4A(2cos()cos( )
= 2cos4A(2cos6A cos5A)
= 4cos4Acos5Acos6A
= right side , thus verified