Question

1) tg (pi/12)
2)-sin7.sin23+cos23.cos7

Answer 1

$tg \frac{x}{2} = \frac{sinx}{1+cosx}$

$tg \frac{ \pi }{12} = \frac{sin \frac{ \pi }{6} }{1+cos \frac{ \pi }{6} } = \frac{ \frac{1}{2} }{1+ \frac{ \sqrt{3} }{2} } = \frac{1}{2}: \frac{ \sqrt{3}+2 }{2} = \frac{1}{2} * \frac{2}{2+ \sqrt{3} } = \frac{1}{2+ \sqrt{3} } =2- \sqrt{3}$

$-sin7^\circ sin23^\circ +cos23^\circ cos7^\circ =cos23^\circ cos7^\circ -sin7^\circ sin23^\circ =$$cos(23^\circ +7^\circ )=cos30^\circ = \frac{ \sqrt{3} }{2}$