Question

тригонометрия 9 класс​

Answer 1

1)

$ctg\alpha \cdot sin\alpha \cdot cos\alpha +4cos^2\alpha =$

         $ctg\alpha =\frac{cos\alpha }{sin\alpha }$

$=\frac{cos\alpha }{sin\alpha } \cdot sin\alpha \cdot cos\alpha +4cos^2\alpha =cos^2\alpha +4cos^2\alpha =5cos^2\alpha$

2)

$sin^2\alpha -1+cos^2\alpha =$

       $sin^2\alpha +cos^2\alpha =1$

$=1-1=0$

3)

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

4)

$tg\alpha\cdot ctg\alpha-sin^2\alpha =\frac{sin\alpha }{cos\alpha } \cdot \frac{cos\alpha }{sin\alpha } -sin^2\alpha =1-sin^2\alpha =(sin^2\alpha +cos^2\alpha) -sin^2\alpha =\\\\=cos^2\alpha$

5)

$1-cos^2\alpha +4sin^2\alpha =(sin^2\alpha +cos^2\alpha) -cos^2\alpha +4sin^2\alpha =\\\\=5sin^2\alpha$