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mafiozo [28]
1 year ago
13

Simplify using trigonometric identities 2sinθ - sin2θ cosθ

Mathematics
1 answer:
Anit [1.1K]1 year ago
8 0

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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Step-by-step explanation:

<u>We can't multiply.</u>

<u>We got to count up by 12's for each 1/2 hour.</u>

12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168.

<u>Simplified:</u>

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<u>Estimate:</u>

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  • 24 = 1 hour
  • 36 = 1 1/2 hours
  • 48 = 2 hours
  • 60 = 2 1/2 hours
  • 72 = 3 hours
  • 84 = 3 1/2 hours
  • 96 = 4 hours
  • 108 = 4 1/2 hours
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