Question

Упростите выражение
sin^2a(1+ctg a)+ cos^2 a(1 - tg a) +7

Answer 1

$sin^{2} alpha (1+ctg alpha )+cos^{2} alpha (1-tg alpha )+7=$
$=sin^{2} alpha +sin^{2} alpha* frac{cos alpha }{sin alpha } +cos^{2} alpha -cos^{2} alpha* frac{sin alpha }{cos alpha }+7=$
$=1+sin alpha *cos alpha -sin alpha *cos alpha +7=8$

Answer 2

=sin^2a+sin^2a*(cosa/sina)+cos^2a-cos^2a*(sina/cosa)=sin^2a+sina*cosa+cos^2-sina*cosa=sin^2a+cos^2=1

Answer 3

1+7=8