How can I determine the exact values for tan75?

1 Answer
May 28, 2015

tan(75^@) = tan (90^@ - 15^@) = cot(15^@) = 1/(tan(15^@)tan(75)=tan(9015)=cot(15)=1tan(15)

tan(15^@) = tan(30^@/2)tan(15)=tan(302)

= (sin(30^@))/(1+cos(30^@))=sin(30)1+cos(30)

= (1/2)/(1+sqrt(3)/2)=121+32

= 1/(2+sqrt(3)=12+3

So
tan(75^@) = 1/tan(15^@) = 2+sqrt(3)tan(75)=1tan(15)=2+3