` tan .(13pi)/(12) ` का मान ज्ञात कीजिए।

Options

A. `(3- sqrt(3))`
B. `(2- sqrt(7))`
C. `(2- sqrt(3))`
D. `(2- sqrt(5))`

Answer

C

Explanation

` tan .(13pi)/(2)= tan .(pi+ (pi)/(12))`
` = tan .(pi)/(12) = tan 15^(@)`
` = tan (45^(@) - 30^(@))`
` = (tan 45^(@) - tan 30^(@))/(1+ tan 45^(@) tan 30^(@)) = (1- (1)/(sqrt(3)))/(1+ (1)/(sqrt(3))) =(sqrt(3)-1)/(sqrt(3)+1)`
`=((sqrt(3)-1)(sqrt(3)-1))/((sqrt(3)+1)(sqrt(3)-1)) =(4- 2sqrt(3))/(2)`
`= (2- sqrt(3))`