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July 28, 2016
Posted by **Ashten** on Monday, January 24, 2011 at 2:56pm.

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

identities should be used.

- trig -
**Reiny**, Monday, January 24, 2011 at 3:11pmI 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