Sin (A + B )≡sin Acos B+cosAsinB, sin (A −B )≡sin Acos B-cosAsinB.

a)Prove that . sin (A + B )+sin (A −B ) ≡ 2sinAcosB.

b)Hence Prove that sin P +sin Q≡ 2sin ((P + Q)/2)cos ((P -Q)/2)

(c ) Hence or otherwise , show that sin 5θ+ 2sin3θ +sin θ ≡ 4 sin3θ 〖cos〗^2 θ

(d ) Solve to the nearest 0.1º , for 0º ≤ θ ≤ 90º ,the equation

sin 5θ + 2sin 3θ +sin θ = 3〖cos〗^2 θ