Question

Find all solutions to the equation sin(3x)cosx+sinx cos(3x)=0 on the interval [0,2pi]

a- x=0,pi/4,pi/2,3pi/4,pi,3pi/2,2pi
b- x=0,pi/2,pi,3pi/2,2pi
c- x=0,pi,2pi
d- x=0,pi/2,3pi/2

Answer 1

Explanation:

Please have in mind that sin(A - B) = sin(A)cos(B) - cos(A)sin(B)

So what we do is:

sin(3x)cos(x) - sin(x)cos(3x) = 0 => sin(3x - x) = 0

sin(2x) = 0

2x = 0, π, 2π, 3π, 4π

x = 0, π/2, π, 3π/2, 2π