Question

How do you find the exact value of the expression `(tan((5pi)/4)-tan(pi/12))/(1+tan((5pi)/4)tan(pi/12))`?

Answer 1

`sqrt3/3`

Explanation:

`"note that"`

`•color(white)(x)tan(A-B)=(tanA-tanB)/(1+tanAtanB)`

`"the given expression is in this form"`

`=tan((5pi)/4-pi/12)=tan((7pi)/6)`

`tan((7pi)/6)=tan(pi/6)=1/sqrt3=sqrt3/3`