Question

упростите выражение (срочно)
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Answer 1

1 - sin²α + ctg²αsin²α = 1 - sin²α + cos²α = cos²α + cos²α = 2cos²α;

$\frac{cos^2\alpha-ctg^2\alpha}{sin^2\alpha-tg^2\alpha}=\frac{cos^2\alpha(1-\frac{1}{sin^2\alpha})}{sin^2\alpha(1-\frac{1}{cos^2\alpha})}=\frac{cos^2\alpha(\frac{sin^2\alpha-1}{sin^2\alpha})}{sin^2\alpha(\frac{cos^2\alpha-1}{cos^2\alpha})}=\frac{cos^2\alpha(\frac{cos^2\alpha}{sin^2\alpha})}{sin^2\alpha(\frac{sin^2\alpha}{cos^2\alpha})}=\frac{cos^4\alpha\cdot cos^2\alpha}{sin^4\alpha\cdot sin^2\alpha}=\frac{cos^6\alpha}{sin^6\alpha}=ctg^6\alpha\)$