Question

Question #573d2

Answer 1

`(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`