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2 years ago

5

In a bag of trail mix, there are 5 cups of nuts for every 2 cups of chocolate candies. If there are 12 cups of nuts in a bag of

trail mix, how many cups of chocolate candies will there be?

1 answer:

Katyanochek1 [597]2 years ago

7 0

Answer:

5

Step-by-step explanation:

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Simplify using trigonometric identities<br> 2sinθ - sin2θ cosθ

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Double angle identity for sine:

$\sin(2x) = 2 \sin(x) \cos(x)$

$\implies 2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta)$

Factorize the left side.

$2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta) = 2 \sin(\theta) \left(1 - \cos^2(\theta)\right)$

Pythagorean identity:

$\cos^2(x) + \sin^2(x) = 1$

$\implies 2 \sin(\theta) \left(1 - \cos^2(\theta)\right) = 2 \sin^3(\theta)$

so that

$\boxed{2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin^3(\theta)}$

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