Question

calcule tg 105°, sabendo que tg 60°=√3 e que tg 45° = 1.

Answer 1

$tg105 ^{o} =tg(60 ^{o} +45 ^{o})= \frac{tg60 ^{o}+tg45 ^{o} }{1+tg60 ^{o}.tg45 ^{o} } \\ = \frac{ \sqrt{3}+1 }{1- \sqrt{3}.1 } = \frac{1+ \sqrt{3} }{1- \sqrt{3} } } = \frac{(1+ \sqrt{3})(1+ \sqrt{3}) }{(1- \sqrt{3})(1+ \sqrt{3} ) } = \frac{1+2 \sqrt{3}+3 }{1- 3\sqr} } = \frac{4+2 \sqrt{3} }{-2} =-(2+ \sqrt{3} )$