trig
posted by Ashten on .
find all values of x on interval 02pi.
(sin4x)(cos7x)=(cos4x)(sin7x)
identities should be used.

I see use of the identity
sin(AB) = 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