Question

prove sin(2pi-x)=-sinx

Answer 1

To prove that sin(2π - x) = -sin(x), we will use the following trigonometric identity:

sin(π - θ) = - sin(θ)

Taking θ = (2π - x), we have:

sin(π - (2π - x)) = - sin(2π - x)

simplifying, we get:

sinπ + sin(2π - x) = - sin(2π - x)

Since sinπ = 0, we have:

0 + sin(2π - x) = - sin(2π - x)

simplifying, we get:

sin(2π - x) = - sin(2π - x)

Hence, we have proved that sin(2π - x) = -sin(x).