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Lady bird [3.3K]
3 years ago
6

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)
Mathematics
1 answer:
schepotkina [342]3 years ago
5 0

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) = 2cos(\frac{5\theta+3\theta}{2})sin(\frac{5\theta-3\theta}{2})

= 2cos(4\theta)sin(\theta) [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 = \frac{90}{4}

θ = 22.5°

and (2sinθ - 1) = 0

sinθ = \frac{1}{2}

θ = 30°

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

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