Question

find the value tan105°​

Answer 1

Answer:

sin (105)/cos (105)

Explanation:

tan (105) = sin (105)/cos (105)

i am of class 9 but the answer above is correct

Answer 2

Answer:

The value of tan105° is -(2+√3)

Explanation:

$\tan(105 \degree) \: = \tan(60 \degree + 45 \degree) \\ \\ \star \sf \: using \: formula \: of \: \tan(A+B) \\ \\ \sf \tan(A+B) = \frac{\tan A + \tan B}{1 -\tan A \tan B } \\ \\ \tan(60 \degree + 45 \degree) = \frac{\tan 60 \degree + \tan 45 \degree}{1 -\tan 60 \degree \tan 45 \degree } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \frac{ \sqrt{3 } + 1 }{1 - \sqrt{3}.1 } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \frac{ {\sqrt{3} + 1}^{2} }{1 - 3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : = - (2 + \sqrt{3} )$

Hence, the value of tan105° is -(2+√3)