Question #573d2

1 Answer
Mia
Sep 21, 2016

(3-sqrt(3))/6

Explanation:

In the given trigonometric expression first we must light on some formulas included :

cos((5pi)/6)=cos(pi-(pi/6))
And we know that
cos(pi-alpha)=-cos(alpha)
So,
color(blue)(cos((5pi)/6)=cos(pi-pi/6)= -cos(pi/6)=-sqrt(3)/2

Now we have:
tan((7pi)/6)=tan(pi+pi/6)=tan(pi/6)
Knowing the formula that says:
tan(pi+alpha)=tan(alpha)
We have:
color(red)(tan((7pi)/6)=tan(pi/6)=sqrt(3)/3)

Let's substitute the answers in the expression given above:
sin(pi/6)+cos((5pi)/6)+tan((7pi)/6)
=1/2+color(blue)(-sqrt(3)/2)+color(red)(sqrt(3)/3)
=(3-sqrt(3))/6

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