Question

упростите выражение (срочно)
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Answer 1

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

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