Using angle sum and difference identities what would be

Question

sin375.?

Answer 1

sin(375) = sin(360 + 15).

Remenber that : sin(360 + θ) = sin(θ)

sin(375) = sin(15).

sin(15) = sin(45 - 30)

Use difference formula : sin(A - B) = sinAcosB - cosAsinB.

sin(15) = sin(45 - 30)

= sin(45) cos(30) - cos(45)sin(30)

= (1/√2)(√3/2) - (1/√2)(1/2)

= (√3 - 1) / 2√2.

Therefore, sin(375) = (√3 - 1) / 2√2.