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Решите задачу:

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