Solve the equation by first using a sum-to-product formula. (enter your answers as a comma-separated list. let k be any integer. round terms to three decimal places where appropriate.) sin(5θ) − sin(3θ) = cos(4θ)

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) =

= [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 =

θ = 22.5°

and (2sinθ - 1) = 0

sinθ =

θ = 30°

Therefore, solutions of the equation are 22.5°, 30°

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step-by-step explanation: