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


identities should be used.

  • trig -

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

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

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