Question

Round to four decimal places. Do not use spaces in your answer. tan75° =

Answer 1

Answer:

Value of tan 75° = 3.7317

Step-by-step explanation:

To find its value we use the following formula,

$tan(a+b)=\frac{tan\,a+tan\,b}{1-tan\,a\:tan\b}$

we also use value of tan 30° = 1/√3  and tan 45° = 1  and √3 =1.7321

$tan\,75=tan\,(45+30)=\frac{tan\,45+tan\,30}{1-tan\,45\:tan\,30}$

               $=\frac{1+\frac{1}{\sqrt{3}}}{1-1\times\frac{1}{\sqrt{3}}}$

               $=\frac{\frac{\sqrt{3}+1}{\sqrt{3}}}{\frac{\sqrt{3}-1}{\sqrt{3}}}$

               $=\frac{\sqrt{3}+1}{\sqrt{3}-1}$

               $=\frac{1.7321+1}{1.7321-1}$

               $=\frac{2.7321}{0.7321}$

               $=3.7317$

Therefore, Value of tan 75° = 3.7317

Answer 2

Better you use calculator:
tan75° = 3.7321