Question

what is the value of tan 75° + cot 75°​

Answer 1

So, we will just proceed and will see what can be the end of the solution.

Let's proceed without fear.

tan 75° + cot 75°

$= \: tan \: 75° + \: \frac{1}{ \tan75° }$

$= \frac{ {tan}^{2}75° + 1 }{tan \: 75°}$

$= { {sec}^{2}75° } \: \times \frac{1}{tan \: 75°}$

$= \frac{1}{ {cos}^{2}75° } \times \frac{cos \: 75°}{ \: sin \: 75°}$

= sec 75° × cosec 75°

Putting the values of sec 75° and cosec 75° (approx.) in their places, we get :

sec 75° × cosec 75°

= 3.9 × 1.03

= 4.017

= 4 (approx.)