Question

Выражения : 1)sin(-альфа)/cos^2(-альфа)-1 2)sin^2(-альфа)-1/cos(-альфа) 3sin^2альфа-1+cos^2альфа+(1-sinальфа)(1+sinальфа) 4)2sin^2альфа-1/1-2cos^2альфа 5)cos^2альфа-1/3-3sin^2альфа 6)4/sin^2альфа-4 ctg^2альфа

Answer 1

$1) \frac{sin(- \alpha )}{cos ^{2}(- \alpha ) - 1} = \frac{-sin \alpha }{cos ^{2} \alpha - 1 } = \frac{-sin \alpha }{-sin ^{2} \alpha } = \frac{1}{ sin \alpha } = sin ^{-1} \alpha$

$2) \frac{sin ^{2}(- \alpha )-1 }{cos(- \alpha )} = \frac{sin ^{2} \alpha - 1 }{cos \alpha } = \frac{-cos^{2} \alpha }{cos \alpha } = -cos \alpha$

$3) sin ^{2} \alpha - 1 + cos ^{2} \alpha + (1 - sin ^{2} \alpha )(1 + sin ^{2} \alpha ) =$ $-cos ^{2} \alpha + cos ^{2} \alpha +1 - sin ^{2} \alpha = cos ^{2} \alpha$

$4) \frac{2sin ^{2} \alpha - 1 }{1 - 2cos ^{2} \alpha } = \frac{- cos ^{2 } \alpha + sin ^{2} \alpha }{sin ^{2} \alpha - cos ^{2} \alpha } = 1$

$5) \frac{cos ^{2} \alpha - 1 }{3 - 3 sin^{2} \alpha } = \frac{-sin ^{2} \alpha }{3cos ^{2} \alpha } = -\frac{1}{3} tg ^{2} \alpha$

$6) \frac{4}{sin ^{2} \alpha } - 4ctg ^{2} \alpha = \frac{4}{sin ^{2} \alpha } -\frac{4cos ^{2} \alpha }{sin ^{2} \alpha } = \frac{4 - 4cos ^{2} \alpha }{sin ^{2} \alpha } = \frac{4sin ^{2} \alpha }{sin ^{2} \alpha } = 4$