Question

Given that cos(A+B)=cosA.cosB-sinA.sinB. Find the value of cos75

Answer 1

cos75 can be written as cos(45+30)
now this can be further simplified as
cos45.cos30-sin45.sin30
(1/√2).(√3/2)-(1/√2).(1/2)
taking 1/√2 as common
1/√2{√3/2-1/2}
1/√2×(√3-1)/2
(√3-1)/2√2
hope you like the solution

Answer 2

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