Question

Нужна . (sin^2b - cos^2b + 1)/sin^2b cos80 + cos40 - cos20= 0 (кроме нуля все в градусах) буду , если .

Answer 1

$\frac{ sin^{2} \beta -cos^{2} \beta +1 }{sin ^{2} \beta } = \frac{ sin^{2} \beta -(1- sin^{2} \beta) +1 }{sin^{2} \beta } = \frac{ sin^{2} \beta -1+ sin^{2} \beta +1 }{ sin^{2} \beta } = \frac{2* sin^{2} \beta }{ sin^{2} \beta } =2$

cos80°+cos40°-cos20°=(cos80°+cos40°)-cos20°=
$=2*cos \frac{ 80^{0}+ 40^{0} }{2}*cos \frac{ 80^{0} - 40^{0} }{2} -cos20°=$
=2*cos60°*cos20°-cos20°=2*cos20° *(2*cos60°-1)=2*cos20° *(1/2-1)=2*(-1/2)*cos20°=-cos20°