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lenaalekseichuk
@lenaalekseichuk
August 2022
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Доказать тригонометрическое тождество
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sonata85ua
Ответ:
Объяснение:
а)
b)
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Answers & Comments
Ответ:
Объяснение:
а)![\frac{sin^2\alpha + (1+cos\alpha)^2 }{(1+cos\alpha)*sin\alpha } =\frac{sin^2\alpha + 1+2cos\alpha +cos^2\alpha }{(1+cos\alpha)*sin\alpha} =\frac{1+1+2cos\alpha }{(1+cos\alpha)*sin\alpha} =\frac{2(1+cos\alpha )}{(1+cos\alpha)*sin\alpha} =\frac{2}{sin\alpha } \frac{sin^2\alpha + (1+cos\alpha)^2 }{(1+cos\alpha)*sin\alpha } =\frac{sin^2\alpha + 1+2cos\alpha +cos^2\alpha }{(1+cos\alpha)*sin\alpha} =\frac{1+1+2cos\alpha }{(1+cos\alpha)*sin\alpha} =\frac{2(1+cos\alpha )}{(1+cos\alpha)*sin\alpha} =\frac{2}{sin\alpha }](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5E2%5Calpha%20%20%2B%20%281%2Bcos%5Calpha%29%5E2%20%7D%7B%281%2Bcos%5Calpha%29%2Asin%5Calpha%20%7D%20%20%20%3D%5Cfrac%7Bsin%5E2%5Calpha%20%20%2B%201%2B2cos%5Calpha%20%2Bcos%5E2%5Calpha%20%7D%7B%281%2Bcos%5Calpha%29%2Asin%5Calpha%7D%20%3D%5Cfrac%7B1%2B1%2B2cos%5Calpha%20%7D%7B%281%2Bcos%5Calpha%29%2Asin%5Calpha%7D%20%3D%5Cfrac%7B2%281%2Bcos%5Calpha%20%29%7D%7B%281%2Bcos%5Calpha%29%2Asin%5Calpha%7D%20%3D%5Cfrac%7B2%7D%7Bsin%5Calpha%20%7D)
b)![\frac{sin\alpha*cos\alpha +sin\alpha }{cos\alpha(1+cos\alpha) } =\frac{sin\alpha(cos\alpha+1) }{cos\alpha(1+cos\alpha)} = \frac{sin\alpha }{cos\alpha } =tg\alpha \frac{sin\alpha*cos\alpha +sin\alpha }{cos\alpha(1+cos\alpha) } =\frac{sin\alpha(cos\alpha+1) }{cos\alpha(1+cos\alpha)} = \frac{sin\alpha }{cos\alpha } =tg\alpha](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5Calpha%2Acos%5Calpha%20%2Bsin%5Calpha%20%20%7D%7Bcos%5Calpha%281%2Bcos%5Calpha%29%20%20%7D%20%3D%5Cfrac%7Bsin%5Calpha%28cos%5Calpha%2B1%29%20%20%7D%7Bcos%5Calpha%281%2Bcos%5Calpha%29%7D%20%20%3D%20%5Cfrac%7Bsin%5Calpha%20%7D%7Bcos%5Calpha%20%7D%20%20%3Dtg%5Calpha)