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[tex] \frac{cos ^{2} \alpha }{1+tg ^{2} \alpha } - \frac{sin ^{2} \alpha }{1+ctg ^{2} \alpha } [/tex]
[tex] \frac{cos ^{2} \alpha }{1+tg ^{2} \alpha } - \frac{sin ^{2} \alpha }{1+ctg ^{2} \alpha } [/tex]
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Cos²a:(1+sin²a/cos²a)-sin²a:(1+cos²a/sin²a)==cos²a*cos²a/(cos²a+sin²a)-sin²a*sin²a/(sin²a+cos²a)=cos^4a-sin^4a=
=(cos²a-sin²a)(cos²a+sin²a)=cos2a