Question

Use a half-angle identity to fifd the exact value of sin 75º

Answer 1

Answer:sin75=√(2+√3)/2

Explanation:

Cosx=1-2sin^2(x/2) let x=150

Cos150=1-2sin^2(150/2) cos150=-√3/2

-(√3)/2=1-2sin^2(75)

2sin^2(75)=1+(√3)/2

2sin^2(75)=(2+√3)/2

Cross multiply

2x2sin^2(75)=2+√3

4sin^2(75)=2+√3

sin^2(75)=(2+√3)/4

Take square root of both sides

sin75=√(2+√3)/√4

sin75=√(2+√3)/2