Question

tan 7pi/12 + cot 5pi/12

Answer 1

write
\[7\pi/12=\pi/4+\pi/6~~ then\\evaluate ~~\tan(\pi/4+\pi/6)~~using~~\tan(a+b)\]

Answer 2

\[\tan(a+b)=\frac{ tana+tanb }{ 1-tana*tanb }\]

Answer 3

use this :)

Answer 4

and
use the same procedure for cot
\[\cot(a+b)=\frac{ cota*cotb-1 }{ cota+cotb }\]

Answer 5

so for tan
\[\tan(\pi/4+\pi/6)=\frac{ \tan(\pi/4)+\tan(\pi/6) }{ 1-\tan(\pi/4)*\tan(\pi/6) }\]
and fot cot\[\cot(\pi/4+\pi/6)=\frac{ \cot(\pi/4)*\cot(\pi/6)-1 }{ \cot(\pi/4)+\cot(\pi/6)}\]
now just substitute the values and u'll get ur answer :)

Answer 6

thanks

Answer 7

oops tmy mistake
but yeah the process will be same
\[for ~(7 \pi/12)=(\pi/4)+(\pi/3)~~and ~~for ~~5\pi/12=\pi/4+\pi/6\]

Answer 8

so
\[\tan(\pi/4+\pi/3)+\cot(\pi/4+\pi/6)\]
now jusu use those formula i wrote above

Answer 9

*just