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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