Write the following product as a sum cos9cos6 Write the foll

Write the following product as a sum.

cos(9)cos(6)

Write the following sum as a product. (You may need to use a Cofunction or Even/Odd identity as well.)

sin(2) sin(5)

cos (9 theta) cos (6 theta)

cos a cos b = 1/2(cos(a+b)+ cos(a-b))

So we get

1/2(cos (9 theta + 6 theta) + cos (9 theta - 6 theta)) = 1/2(cos 15 theta + cos 3 theta)

sin2 theta - sin 5 theta

sin a - sin b=2cos(a+b)/2 sin(a-b)/2

so we get

-2 cos (7theta)/2 sin(3theta)/2