Find the exact value of the expression sin 15 degree cos 105

Find the exact value of the expression. sin 15 degree cos 105 degree + cos 15 degree sin 105 degree 1/4 squareroot 3/2 - squareroot 3/2 - 1/2

Solution

Sin 15 cos 105 + cos 15 sin 105

This is of the form

Sin A cos B + cos A sin B which is equal to sin(A+B)

Therefore

Sin 15 cos 105 + cos 15 sin 105= sin(15+105) =sin 120= sqrt3/2

Correct option is B