Question

Sin 15°=? sin 105°=? tg 75°=? ctg 15°=?

Answer 1

Sin15°=sin(45°-30°)=sin45°cos30°-cos45°sin30°=$\frac{ \sqrt{2} }{2} * \frac{ \sqrt{3} }{2} - \frac{ \sqrt{2} }{2} * \frac{1}{2} = \frac{ \sqrt{2}( \sqrt{3}-1 ) }{4}$

sin105°=sin(45°+60°)=sin45°cos60°+cos45°sin60°=$\frac{ \sqrt{2} }{2}* \frac{1}{2} + \frac{ \sqrt{2} }{2} * \frac{ \sqrt{3} }{2} = \frac{ \sqrt{2} (\sqrt{3}+1) }{4}$

tg75°=tg(45°+30°)=$\frac{tg45+tg30}{1-tg45*tg30}= \frac{1+ \frac{2}{ \sqrt{3} } }{1- \frac{1}{ \sqrt{3} } } = \frac{ \sqrt{3} +1}{ \sqrt{3}-1 }$

ctg15=ctg(45-30)=$\frac{-1-ctg45*ctg30}{ctg45-ctg30}= \frac{-1- \sqrt{3} }{1- \sqrt{3} }$