Question

помогите решить!!!Так как не могу решить,прошу)))

Answer 1

1)

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

2)

$tg(\alpha)+ctg(\alpha)=tg(\alpha)+ \frac{1}{tg(\alpha)} = \frac{tg(\alpha)^{2}+1}{tg(\alpha)} \\ \\ \frac{ \frac{sin(\alpha)^{2}}{cos(\alpha)^{2}}+1 }{ \frac{sin(\alpha)}{cos(\alpha)} } = \frac{ \frac{sin(\alpha)^{2}+cos(\alpha)^{2}}{cos(\alpha)^{2}} }{ \frac{sin(\alpha)}{cos(\alpha)} } = \frac{1}{cos(\alpha)*sin(\alpha)} = \frac{1}{0,6}= \frac{1}{ \frac{5}{3} } = \frac{5}{3}=1 \frac{2}{3}$

3)

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

4)

$sin(\pi-\alpha)+cos(3\pi+\alpha)+sin(-\alpha)+cos(\alpha) \\ \\ sin(\alpha)-cos(\alpha)-sin(\alpha)+cos(\alpha) \\ \\ -cos(\alpha)+cos(\alpha)=0$