Answer:
Solutions of the equation are 22.5°, 30°.
Step-by-step explanation:
The given equation is sin(5θ) - sin(3θ) = cos(4θ)
We take left side of the equation
sin(5θ) - sin(3θ) = [tex]2cos(\frac{5\theta+3\theta}{2})sin(\frac{5\theta-3\theta}{2})[/tex]
= [tex]2cos(4\theta)sin(\theta)[/tex] [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 = [tex]\frac{90}{4}[/tex]
θ = 22.5°
and (2sinθ - 1) = 0
sinθ = [tex]\frac{1}{2}[/tex]
θ = 30°
Therefore, solutions of the equation are 22.5°, 30°
