Answer:
Value of tan 75° = 3.7317
Step-by-step explanation:
To find its value we use the following formula,
[tex]tan(a+b)=\frac{tan\,a+tan\,b}{1-tan\,a\:tan\b}[/tex]
we also use value of tan 30° = 1/√3 and tan 45° = 1 and √3 =1.7321
[tex]tan\,75=tan\,(45+30)=\frac{tan\,45+tan\,30}{1-tan\,45\:tan\,30}[/tex]
[tex]=\frac{1+\frac{1}{\sqrt{3}}}{1-1\times\frac{1}{\sqrt{3}}}[/tex]
[tex]=\frac{\frac{\sqrt{3}+1}{\sqrt{3}}}{\frac{\sqrt{3}-1}{\sqrt{3}}}[/tex]
[tex]=\frac{\sqrt{3}+1}{\sqrt{3}-1}[/tex]
[tex]=\frac{1.7321+1}{1.7321-1}[/tex]
[tex]=\frac{2.7321}{0.7321}[/tex]
[tex]=3.7317[/tex]
Therefore, Value of tan 75° = 3.7317
