Question

HELP PLEASE!!
Select the correct answer.
What is the exact value of tan 75°?

Answer 1

`\tt B. \ \ \ \cfrac{1+(√(3))/(3)}{1-(√(3))/(3)}`

Explanation:

`\displaystyle\tt \tan75^o=\tan(45^o+30^o)=(\tan45^o+\tan30^o)/(1-\tan45^o\cdot\tan30^o) =(1+(√(3))/(3))/(1-(√(3))/(3))`

Answer 2

For this case we have to define that:

`tg (x + y) = \frac {tg (x) + tg (y)} {1-tg (x) * tg (y)}`

So, according to the problem we have:

`tg (45 + 30) = \frac {tg (45) + tg (30)} {1-tg (45) * tg (30)}`

By definition we have to:

`tg (45) = 1\\tg (30) = \frac {\sqrt {3}} {3}`

Substituting we have:

`tg (45 + 30) = \frac {1+ \frac {\sqrt {3}} {3}} {1-1 * \frac {\sqrt {3}} {3}}\\tg (45 + 30) = \frac {1+ \frac {\sqrt {3}} {3}} {1- \frac {\sqrt {3}} {3}}`

Answer:

option B