Question

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

Answer 1

Answer:

$\tt B. \ \ \ \cfrac{1+\frac{\sqrt{3}}{3}}{1-\frac{\sqrt{3}}{3}}$

Step-by-step explanation:

$\displaystyle\tt \tan75^o=\tan(45^o+30^o)=\frac{\tan45^o+\tan30^o}{1-\tan45^o\cdot\tan30^o} =\frac{1+\frac{\sqrt{3}}{3}}{1-\frac{\sqrt{3}}{3}}$

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