Solutions of the equation are 22.5°, 30°.
The given equation is sin(5θ) - sin(3θ) = cos(4θ)
We take left side of the equation
sin(5θ) - sin(3θ) = 2cos ((5θ+3θ)/2) (sin(5θ-3θ)/2)
=2cos4θsinθ [From sum-product identity]
Now we can write the equation as
2cos(4θ)sin(θ) = cos(4θ)
2cos(4θ)sinθ - cos(4θ) = 0
cos(4θ)[2sinθ - 1] = 0
cos(4θ) = 0
4θ = 90°
θ = 90/4
θ = 22.5°
and (2sinθ - 1) = 0
sinθ = 1/2
θ = 30°
Therefore, solutions of the equation are 22.5°, 30°
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