5. . Sum-to-Product Formulas sin a + sin 3 = 2 sin a + B a - B COS a + 3 a - 2 sin a - sin 3 = 2 cos 2 sin 2 a + B ON cos a + cos B = 2 cos a - B a + B COS 2 2 ; cos a - cos 3 = -2 sin B sin 2 2 . Product-to-Sum Formulas sin a cos B = = [sin(a + 3) + sin(a - B)]; cos a cos B = - cos(a + B) + cos(a - B)]; sin a sin 3 = -~ [cos(a + B) - cos(a - B)]. Answer the following questions. (a) Find the exact value of sin 105 cos 75; (b) Prove sin 2x + sin 4x = cot x. cos 2x - cos 4x