Question

помогите прошу...171-172 задания

Answer 1

Номер 171
1)$sin^{2} alpha +cos^{2} alpha +tg ^{2} alpha - frac{1}{cos^{2} alpha } =sin^{2} alpha +cos^{2} alpha + frac{sin ^{2} alpha }{cos^{2} alpha } - frac{1}{cos^{2} alpha}$$=1+ frac{sin^{2} alpha-1}{cos^{2} alpha} = frac{cos^{2}alpha+sin^{2}alpha-1}{cos^{2}alpha} =sin^{2}alpha-1=-cos^{2} alpha$
2) $2- frac{1}{sin^{2} alpha } +ctg^{2} alpha =2- frac{1}{sin^{2} alpha } + frac{cos^{2} alpha }{sin^{2} alpha } = frac{2sin^{2} alpha -1+cos ^{2} alpha }{sin^{2} alpha } = 2-1$$+cos^{2} alpha =cos^{2} alpha +1$
Номер 172
1) $sin^{2} alpha=1-cos^{2} alpha =1- frac{1}{4}= frac{3}{4}$
$sinalpha= sqrt{ frac{3}{4} } = frac{ sqrt{3}}{2}$
$tg=frac{sin alpha }{cos alpha } = frac{ frac{ sqrt{3}}{2} }{ frac{1}{2} } = frac{ 2sqrt{3} }{2}= sqrt{3}$
2) $cos x^{2} =1-sin^{2} =1- frac{3}{4}= frac{1} }{4}$
$cos alpha = sqrt{ frac{1}{4} } = frac{1}{2}$
$tg alpha = frac{sin alpha }{cos alpha } = frac{ frac{ sqrt{3} }{2} }{ frac{1}{2} } = frac{2 sqrt{3} }{2} = sqrt{3}$
3) $cos^{2} alpha =1-sin^{2} alpha =1- frac{1}{16} = frac{15}{16}$
$cos alpha = sqrt{ frac{15}{16} } = frac{ sqrt{15} }{4}$
$tg alpha= frac{sin alpha }{cos alpha }= frac{ frac{1}{4} }{ frac{ sqrt{15} }{4} }= frac{4}{4 sqrt{15} } = frac{1}{ sqrt{15} } = frac{ sqrt{15} }{15}$