Question

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

tan75° =

Answer 1

Better you use calculator:
tan75° = 3.7321

Answer 2

Value of tan 75° = 3.7317

Explanation:

To find its value we use the following formula,

`tan(a+b)=(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)=(tan\,45+tan\,30)/(1-tan\,45\:tan\,30)`

`=(1+(1)/(√(3)))/(1-1*(1)/(√(3)))`

`=((√(3)+1)/(√(3)))/((√(3)-1)/(√(3)))`

`=(√(3)+1)/(√(3)-1)`

`=(1.7321+1)/(1.7321-1)`

`=(2.7321)/(0.7321)`

`=3.7317`

Therefore, Value of tan 75° = 3.7317