Упростите: [tex]\frac{1}{1-tg^2\alpha}-\frac{1}{1-ctg^2\alpha}[/tex] Правильный ответ [tex]\frac{1}{cos2\alpha}[/tex]. Created by RedBaron. algebra-ru

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Verified answer

$1-tg^2\alpha = 1-\frac{sin^2\alpha}{cos^2\alpha} = \frac{cos2\alpha}{cos^2\alpha}1-ctg^2\alpha = 1-\frac{cos^2\alpha}{sin^2\alpha} = - \frac{cos2\alpha}{sin^2\alpha}$

тогда

$\frac{cos^2\alpha}{cos2\alpha} - (-\frac{sin^2\alpha}{cos2\alpha}) = \frac{1}{cos2\alpha}$

Quintessence

1/(1-tg²α)-1/(1-ctg²α)=cos²α/(cos²α-sin²α)-sin²α/(sin²α-cos²α)=(cos²α+sin²α)/(cos²α-sin²α)=1/cos2α.

Answers & Comments

Verified answer

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