Question

using the formula cos(A+B)=cosAcosB-sinAsinB, evaluate cos75

Answer 1

Step-by-step explanation:

Put A=30° ,B=45°

Cos(A+B)=CosA.CosB-SinA.SinB

Cos(30°+45°)=(Cos 30°×Cos 45°)-(Sin 30°×Sin 45°)

Cos 75°=[(√3/2)×(1/√2)]-[(1/2)×(1/√2)]

             =(√3 / 2√2) - (1 / 2√2)

             =√3-1 / 2√2

∴Cos 75°=√3-1 / 2√2