Find the exact value of each expression cos 105 degree cos

Find the exact value of each expression. cos 105 degree + cos 15 degree = squareroot 2/2 sin 37.5 degree cos 7.5 degree =

Solution

applying sum to products formula

sin a cos b = 1/2 [ sin ( a+ b ) + sin (a-b ) ]

sin 37.5 cos 7.5 = 1/2 [ sin ( 45 ) + sin ( 30 ) ]

= 1/2 [ 1 / sqrt 2 + 1 / 2 ]

= 1/2 sqrt 2 + 1/ 4

= sqrt 2 / 4 + 1/4

= ( sqrt 2 + 1 ) / 4