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![(ctg alpha + 1)^2 + (ctg alpha -1)^2 = \ \ = ctg^2 alpha + 2ctg alpha +1 + ctg^2 alpha -2ctg alpha +1 = \ \ = 2ctg^2 alpha +2 = 2*(ctg^2 alpha +1) = \ \ = 2*( frac{cos^2 alpha }{sin^2 alpha } +1) = 2* frac{cos^2 alpha +sin^2 alpha }{sin^2 alpha } = \ \ =2* frac{1}{sin^2 alpha } = frac{2}{sin^2 alpha } (ctg alpha + 1)^2 + (ctg alpha -1)^2 = \ \ = ctg^2 alpha + 2ctg alpha +1 + ctg^2 alpha -2ctg alpha +1 = \ \ = 2ctg^2 alpha +2 = 2*(ctg^2 alpha +1) = \ \ = 2*( frac{cos^2 alpha }{sin^2 alpha } +1) = 2* frac{cos^2 alpha +sin^2 alpha }{sin^2 alpha } = \ \ =2* frac{1}{sin^2 alpha } = frac{2}{sin^2 alpha }](https://tex.z-dn.net/?f=%28ctg+alpha++%2B+1%29%5E2+%2B+%28ctg+alpha+-1%29%5E2+%3D+%5C+%5C++%3D+ctg%5E2+alpha+%2B+2ctg+alpha+%2B1+%2B+ctg%5E2+alpha+-2ctg+alpha++%2B1+%3D++%5C+%5C+%3D+2ctg%5E2+alpha+%2B2+%3D+2%2A%28ctg%5E2+alpha+%2B1%29+%3D++%5C+%5C+%3D+2%2A%28+frac%7Bcos%5E2+alpha+%7D%7Bsin%5E2+alpha+%7D+%2B1%29+%3D+2%2A+frac%7Bcos%5E2+alpha+%2Bsin%5E2+alpha+%7D%7Bsin%5E2+alpha+%7D+%3D++%5C+%5C+%3D2%2A+frac%7B1%7D%7Bsin%5E2+alpha+%7D+%3D++frac%7B2%7D%7Bsin%5E2+alpha+%7D+)
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