Question #7c036

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Question #7c036

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Answer 1 · 2017-10-28T03:19:35

$x \approx 11.6558890174$ $x~~11.6558890174$ degrees

Explanation:

We start with the given:
$tan (x) sin (20) + sin (20) = 2 tan (x)$ $tan(x)sin(20)+sin(20)=2tan(x)$

Then bring everything with x onto one side, place whatever else on the other side:
$sin (20) = 2 tan (x) - tan (x) sin (20)$ $sin(20)=2tan(x)-tan(x)sin(20)$

Factorise $tan (x)$ $tan(x)$ :
$sin (20) = tan (x) (2 - sin (20))$ $sin(20)=tan(x)(2-sin(20))$

Divide both sides by $(2 - sin (20))$ $(2-sin(20))$ so we leave $tan (x)$ $tan(x)$ alone
$tan (x) = \frac{sin (20)}{2 - sin (20)}$ $tan(x)=sin(20)/(2-sin(20)$

Use the ${tan}^{- 1}$ $tan^-1$ function to make $tan (x)$ $tan(x)$ into just $x$ $x$
$x = {tan}^{- 1} (\frac{sin (20)}{2 - sin (20)})$ $x=tan^-1(sin(20)/(2-sin(20)))$

Plug it into calculator:
$x \approx 11.6558890174$ $x~~11.6558890174$ degrees

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Question #7c036

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