Question

Помогите пожалуйста, буду очень благодарна

Answer 1

1.
$frac{sin(pi - alpha)sin(2pi + alpha)cos(2pi - alpha)}{sin(frac{pi}{2} - alpha){rm ctg}(frac{3pi}{2} + alpha){rm ctg}(pi- alpha)} =frac{sin alphasin alphacos alpha}{cosalpha(-{rm tg},alpha),(-{rm ctg} alpha)}=sin^2alpha.$

2.
$cosalpha=frac{2}{sqrt{5}},,0 textless alpha textless frac{pi}{2}Rightarrow sin alpha =sqrt{1-left(frac{2}{sqrt{5}}right)^2}=frac{1}{sqrt{5}}Rightarrow\ {rm tg}, alpha =frac{1}{2},,{rm tg},beta=frac{1}{3}Rightarrow {rm tg},( alpha -beta)=frac{{rm tg}, alpha -{rm tg},beta}{1+{rm tg}, alpha {rm tg},beta}=$
$=frac{frac{1}{2} -frac{1}{3}}{1+frac{1}{2}cdotfrac{1}{3}}=frac{frac{5}{6}}{1+frac{1}{6}}=frac{5}{7}.$

3.
$frac{2sin alpha -sin2 alpha }{cos alpha -cos^2 alpha -sin^2 alpha } = frac{2sin alpha -2sinalphacos alpha }{cos alpha -1 } =frac{2sin alpha(1-cos alpha) }{cos alpha -1 } =-2sin alpha$