Answers

2015-01-08T21:32:28+08:00
Tan 135 ( 180 - 45 )

 \frac{tan 180 - tan 45}{1 + ( tan 180 ) ( tan 45 )}

 \frac{ 0 -  \frac{ \sqrt{2} }{2} }{1 + ( 0 ) (  \frac{ \sqrt{2} }{2 }) }

 \frac{ \frac{ \sqrt{2} }{2} }{1}

= \frac{ \sqrt{2} }{2}

sorry.. hindi ko makuha yung 165

basta ganito yung solution... baka 135 lang talaga? joke hahaha sorry hindi ako nakatulong T^T

0
2015-01-09T13:19:58+08:00
Note: tan(165)= tan(120+45)
         tan(u+v)=  \frac{tanu+tanv}{1-tanutanv}

Substitute values:
tan(120+45)=  \frac{tan120+tan45}{1-tan120tan45}
tan(165) =  \frac{ \sqrt{3}+1 }{1- \sqrt{3}(1) }
tan(165)= \frac{ \sqrt{3}+1 }{1- \sqrt{3} }

Rationalize (if needed):
 (\frac{\sqrt{3}+1 }{1- \sqrt{3} } )( \frac{1+ \sqrt{3} }{1+ \sqrt{3} } )
= \frac{2 \sqrt{3}+4}{2}
=- \sqrt{3}+2
0