Question

What is the exact value of tan 75°?

1−3√31+3√3


1+3√31−3√3


1+3√1−3√


1−3√1+3√

Answer 1

Answer:

√3+1

------------

√3-1

Explanation:

Tan (75) = Tan (45+30)

Tan 45 + Tan3O

-----------------------

1- Tan45 Tan30

√3+1

---------

√3 -1

Answer 2

Answer:

tan(75°) can be writte as:

tan(30°+45°)

Now, as:

$\tan(x + y) = \frac{ \tan(x) + \tan(y) }{1 - \tan(x). \tan(y) }$

$\tan(75°) = \frac{ \tan(30°) + \tan(45°) }{1 - \tan(30°). \tan(45°) }$

$\tan(75°) = \frac{ \frac{1}{ \sqrt{ 3 } } + 1 }{1 - (1)( \frac{1}{ \sqrt{3} }) }$

$⇒ \tan(75°) = \frac{1 + \sqrt{3} }{ \sqrt{3} - 1 }$

On Rationalising the denominator:

$⇒ \tan(75°) =2 + \sqrt{3}$