Question #7c036

1 Answer
ProfLayton
Oct 28, 2017

x~~11.6558890174 degrees

Explanation:

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

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

Divide both sides by (2-sin(20)) so we leave tan(x) alone
tan(x)=sin(20)/(2-sin(20)

Use the tan^-1 function to make tan(x) into just x
x=tan^-1(sin(20)/(2-sin(20)))

Plug it into calculator:
x~~11.6558890174 degrees

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