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
