find all values of x on interval 0-2pi.

Question

(sin4x)(cos7x)=(cos4x)(sin7x)

identities should be used.

Answer 1

I see use of the identity
sin(A-B) = sinAcosB - cosAsinB

(sin4x)(cos7x)=(cos4x)(sin7x)
(sin4x)(cos7x) - (cos4x)(sin7x) = 0
sin(4x - 7x) = 0
sin (-3x) = 0
but we know that sin(-A) = -sinA
so
sin(-3x) = -sin(3x)

sin(3x) = 0
but sinØ = 0 , Ø = 0,π,2π,3π....
so 3x = 0, π, 2π, 3π, 4π, 5π ,6π, ...
x = 0, π/3, 2π/3, π, 4π/3, 5π/3, and 2π