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Dmitrij [34]
3 years ago
9

Simplify: xy^2(-2x)(3xy)(-4x^2y)1/8x^2y^3

Mathematics
1 answer:
vredina [299]3 years ago
3 0

Answer:

-12x^5 y^4

Step-by-step explanation:

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If you know that \sin\dfrac\pi3=\dfrac12, then you know right away

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###

Otherwise, you can derive the same result. Let \theta=\sin^{-1}\dfrac12, so that \sin\theta=\dfrac12. \sin^{-1} is bounded, so we know -\dfrac\pi2\le\theta\le\dfrac\pi2. For these values of \theta, we always have \cos\theta\ge0.

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\cos^2\theta+\sin^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\left(\dfrac12\right)^2}=\dfrac{\sqrt3}2

Then

\tan\theta=\tan\left(\sin^{-1}\dfrac12\right)=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}=\dfrac{\sqrt3}3

as expected.

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3 years ago
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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