Question #81e80

2 Answers
Thomas J.
Jan 8, 2018

#2sqrt3#

Explanation:

Search up trig exact values. The exact value of #tan45# is #1#, #tan30# is #1/sqrt3#, and #tan60# is #sqrt3#. Solve it like you would a normal equation and #1/(1/sqrt3)# + #sqrt3# is #2sqrt3#

turksvids
Jan 8, 2018

#tan(45^circ)/tan(30^circ) + tan(60^circ) = 2sqrt(3)#

and

#tan(45^circ)/(tan(30^circ) + tan(60^circ))=sqrt(3)/4#

Explanation:

I can't tell from the formatting exactly what you mean, but:

#tan(45^circ) = 1#, #tan(30^circ) = sqrt(3)/3=1/sqrt(3)#, and #tan(60^circ) = sqrt(3)#.

So:

#tan(45^circ)/tan(30^circ) + tan(60^circ)#

#=1/(1/sqrt(3)) + sqrt(3) = sqrt(3)+sqrt(3) = 2sqrt(3)#

On the other hand, if the problem was meant to be:

#tan(45^circ)/(tan(30^circ) + tan(60^circ))#

#=1/(1/sqrt(3)+sqrt(3))#

#= 1/((1+3)/sqrt(3))#

#=sqrt(3)/(4)#

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