Ответ:

Объяснение:

1)

[tex]sin^2\beta -1=sin^2\beta -sin^2\beta -cos^2\beta =-cos^2\beta[/tex]

2)

[tex]sin^2\alpha +cos^2\alpha +ctg^2\alpha =1+ctg^2\alpha=csc^2\alpha[/tex]

3)

[tex]2sin\alpha ctg\alpha -cos\alpha =\frac{2sin\alpha cos\alpha }{sin\alpha } -cos\alpha =2cos\alpha -cos\alpha =cos\alpha[/tex]

4)

[tex]\frac{cos^2\alpha -1}{sin^2\alpha -1} +tg\alpha ctg\alpha =\frac{cos^2\alpha -cos^2\alpha -sin^2\alpha }{sin^2\alpha -cos^2\alpha -sin^2\alpha} +1=tg^2\alpha +1=sec^2\alpha[/tex]

5)

[tex]\frac{tg\alpha cos\alpha }{1+ctg^2\alpha } =\frac{\frac{sin\alpha }{cos\alpha }cos\alpha }{1+\frac{cos^2\alpha }{sin^2\alpha } } =\frac{sin\alpha }{\frac{sin^2\alpha +cos^2\alpha }{sin^2\alpha } } =sin^3\alpha[/tex]

6)

[tex](1+cosx)(1-cosx)=1-cos^2x=cos^2x+sin^2x-cos^2x=sin^2x[/tex]

7)

[tex]ctgx+\frac{sinx}{1+cosx} =\frac{cosx}{sinx} +\frac{sinx}{1+cosx} =\frac{cosx+cos^2x+sin^2x}{sinx(1+cosx)} =\frac{cosx+1}{sinx(1+cosx)} =\frac{1}{sinx} =cscx[/tex]