Question

Вычислите значение выражения 5ctg 13/2п+2cos 21п/4+2sin 41п/4

Answer 1

$5ctgfrac{13pi}{2}+2cos frac{21pi}{4}+2sinfrac{41pi}{4}\ ctgfrac{13pi}{2}=ctg(frac{12pi}{2}+frac{pi}{2})=ctg(6pi+frac{pi}{2})=ctgfrac{pi}{2}=0;\ cos frac{21pi}{4}=cos(frac{20pi}{4}+frac{pi}{4})=cos(5pi+frac{pi}{4})=-cosfrac{pi}{4}=-frac{sqrt2}{2};\ sinfrac{41pi}{4}=sin(frac{40pi}{4}+frac{pi}{4})=sin(10pi+frac{pi}{4})=sinfrac{pi}{4}=frac{sqrt2}{2};\5*0+2*(-frac{sqrt2}{2})+2*frac{sqrt2}{2}=-sqrt2+sqrt2=0.$