Find the solutions of each equation on the interval [0, 2π).
sin(3π/2+x) + sin(3π/2+x) = -2

show how you got the answer i don't understand

x = 0

Step-by-step explanation:

Given sin(3π/2+x) + sin(3π/2+x) = -2

2sin(3π/2+x) = -2

sin(3π/2+x) = -1

clearly x = 0 on satisfies the above equation

We know that sin(3π/2+x) = - cosx

-cosx = -1

cosx = 1 Has only one solution at x=0 in x∈ [0,2π)