Write cos 2x cos 3x as a sum of two trigonometric functions

Write cos 2x cos 3x as a sum of two trigonometric functions Write cos 6x + cos 6x as a product of two trigonometric functions You are given that theta is an angle that satisfies the two conditions tan theta = - 21/20 and sin theta

Solution

cos2x cos 3x

cos A + cos B= 2 cos((A+B)/2) cos((A-B)/2)

or we can also write it as

1/2(cos A + cos B)= cos ((A+B)/2) cos((A-B)/2)

comparing it with given expression we get

A+B/2=3x and A-B/2=2x

A+B=6x and A-B= 4x

solving them we get

A= 5x and B= x

Therefore the required expression is

1/2(cos 5x + cos x)

6. cos 6x + cos 6x

2cos (6x+6x/2) cos(6x-6x/2)

2cos 6x cos 0=2cos 6x