Question

Find the exact value of tangent of 7 times pi over 12 period2 minus radical 32 plus radical 3negative 2 minus radical 3negative 2 plus radical 3

Answer 1

-(2+ square root 3)

Explanation:

took the test and got it right

Answer 2

Given

`\tan(7\pi)/(12)`

Rewrite as:

`=\tan\left((\pi)/(4)+(\pi)/(3)\right)`

Use the trigonometric identity for addition of angles:

`=(\tan\left((\pi)/(4)\right)+\tan\left((\pi)/(3)\right))/(1-\tan\left((\pi)/(4)\right)\tan\left((\pi)/(3)\right))`

Then:

`\begin{gathered} \tan((\pi)/(4))=1 \\ \tan((\pi)/(3))=√(3) \end{gathered}`

Next, substitute the values:

`=(1+√(3))/(1-1\cdot√(3))`

Simplify:

`=(1+√(3))/(1-√(3))`

Multiply by numerator:

`=(\left(1+√(3)\right)\left(1+√(3)\right))/(\left(1-√(3)\right)\left(1+√(3)\right))=(1+√(3)+√(3)+3)/(1+√(3)-√(3)-3)`

Simplify:

`(4+2√(3))/(-2)`

Factor the common term 2 in the numerator:

Answer:

`\begin{equation*} -2-√(3) \end{equation*}`