Question

Чему равен tg 22.5% или sin 22.5%

Answer 1

$tg frac{x}{2}= frac{sinx}{1+cosx} \\tg22,5=tg(45/2)= frac{sin45}{1+cos45}= frac{ frac{ sqrt{2} }{2} }{1+ frac{ sqrt{2} }{2} }= frac{ sqrt{2} }{2+ sqrt{2} }= frac{ sqrt{2} }{ sqrt{2}( sqrt{2}+1 )}= frac{1}{ sqrt{2}+1 } \\sin frac{x}{2}= sqrt{ frac{1-cosx}{2} }\\sin22,5=sin(45/2)=sqrt{ frac{1-cos45}{2} } = sqrt{ frac{1- frac{ sqrt{2} }{2} }{2} }= sqrt{ frac{2- sqrt{2} }{2*2} }=sqrt{ frac{ sqrt{2}( sqrt{2}-1) }{4}}=$

$= frac{ sqrt{ sqrt{2} ( sqrt{2} -1)} }{2}$