Question

50 баллов. С полным и понятным решением.​

Answer 1

Cм. рисунок.

α+β=π

tgα=6/5

ctgα=5/6

tgβ=tg(π-α)=-tgα=-6/5

ctgβ=-5/6

По формуле:

1+tg²α=1/cos²α

cos²α=25/61

1+ctg²α=1/sin²α

sin²α=36/61

cos²β=sin²α=36/61

sin²β=cos²α=25/61

$\frac{sin^2\alpha+sin^2\beta -tg\alpha tg\beta}{cos^{2}\alpha-cos^{2}\beta-ctg\alpha ctg\beta}=\frac{\frac{36}{61}+\frac{25}{61}-\frac{6}{5}\cdot( \frac{5}{6})}{\frac{25}{61}-\frac{36}{61}-\frac{5}{6}\cdot(-\frac{6}{5})  }=\frac{1-1}{-\frac{11}{61}+1 } =0$