Question

Express the following as a sum or difference of two trigonometric function.
2sin×2π/3 cosπ/2​

Answer 1

In trigonometry,

sin (A + B) + sin(A - B) = 2sinAcosB

Given : 2sin 2π/3 cos π/2

let A = 2π/3 and B = π/2

So,

sin (2π/3 + π/2) + sin (2π/3 - π/2) = 2sin 2π/3 cos π/2

sin (7π/6) + sin (π/6) = 2 sin(2π/3) cos(π/2)

Hope, this helps you.