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

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

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

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