Express the given sum or difference as a product of sines an

Express the given sum or difference as a product of sines and or cosines. sin 4theta + sin 8 theta

Solution

sin4 +sin8

sin8+sin4

sinc+sind= 2sin((c+d)/2)cos((c-d)/2)

=2sin((8+4)/2)cos((8-4)/2)

=2sin((12)/2)cos((4)/2)

=2sin(6)cos(2)

so sin4 +sin8=2sin(6)cos(2)