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3 years ago

5

Find the value of x

1 answer:

devlian [24]3 years ago

5 0

X=20
180=7x+x+20
-20. -20
180=7x+x
180=8x
divide by 8
x=20

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Step-by-step explanation:

Given

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$\theta \to$ Quadrant III

Required

Determine $\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

We have:

$\cos(\theta) = -\frac{2}{3}$

We know that:

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

This gives:

$\sin^2(\theta) + (-\frac{2}{3})^2 = 1$

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Take the square roots of both sides

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Calculate $\csc(\theta)$

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So:

$\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}$

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Rationalize

$\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}$

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$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)$

Substitute: $\csc(\theta) = \frac{-3\sqrt 5}{5}$

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Take LCM

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