` tan 105^(@)` का मान क्या है ?

Options

A. ` (sqrt(3)+1)/(sqrt(3)-1)`
B. `(sqrt(3)+1)/(sqrt(3)+1)`
C. `(sqrt(3)+1)/(sqrt(3)+1)`
D. ` (sqrt(3)+2)/(sqrt(3)-1)`

Answer

b

Explanation

` tan 105^(@) = tan (60^(@)+45^(@))`
` = (tan 60^(@) + tan 45^(@))/(1-tan 6-^(@) * tan 45^(@))`
` [ :' tan ( A+B) = (tan A+ tanB)/(1-tan A*tanB)]`
` = (sqrt(3)+1)/(1-sqrt(3)*1)=(sqrt(3)+1)/(1-sqrt(3))`