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ctg^2 b(бета)*(cos^2 b-1)+1![ctg^2 beta = frac{cos^2 beta }{sin^2 beta }
ctg^2 beta = frac{cos^2 beta }{sin^2 beta }](https://tex.z-dn.net/?f=ctg%5E2+beta+%3D+frac%7Bcos%5E2+beta+%7D%7Bsin%5E2+beta+%7D+%0A)
![1=sin^2 beta +cos^2 beta 1=sin^2 beta +cos^2 beta](https://tex.z-dn.net/?f=1%3Dsin%5E2+beta+%2Bcos%5E2+beta+)
![frac{cos^2 beta }{sin^2 beta } *(cos^2 beta -sin^2 beta -cos^2 beta )+sin^2 beta +cos^2 beta =frac{cos^2 beta }{sin^2 beta } *(-sin^2 beta)+sin^2 beta +cos^2 beta=-cos^2 beta +sin^2 beta +cos^2 beta =sin^2 beta frac{cos^2 beta }{sin^2 beta } *(cos^2 beta -sin^2 beta -cos^2 beta )+sin^2 beta +cos^2 beta =frac{cos^2 beta }{sin^2 beta } *(-sin^2 beta)+sin^2 beta +cos^2 beta=-cos^2 beta +sin^2 beta +cos^2 beta =sin^2 beta](https://tex.z-dn.net/?f=+frac%7Bcos%5E2+beta+%7D%7Bsin%5E2+beta+%7D+%2A%28cos%5E2+beta+-sin%5E2+beta+-cos%5E2+beta+%29%2Bsin%5E2+beta+%2Bcos%5E2+beta+%3Dfrac%7Bcos%5E2+beta+%7D%7Bsin%5E2+beta+%7D+%2A%28-sin%5E2+beta%29%2Bsin%5E2+beta+%2Bcos%5E2+beta%3D-cos%5E2+beta+%2Bsin%5E2+beta+%2Bcos%5E2+beta+%3Dsin%5E2+beta+)
tg b+1/1+ctg b, так как
имеем:
![frac{tg beta +1}{1+ frac{1}{tg beta } } = frac{tg beta +1}{ frac{tg beta }{tg beta } + frac{1}{tg beta } }=(tg beta +1): frac{tg beta +1}{tg beta } = frac{(tg beta +1)tg beta }{tg beta +1}=tg beta frac{tg beta +1}{1+ frac{1}{tg beta } } = frac{tg beta +1}{ frac{tg beta }{tg beta } + frac{1}{tg beta } }=(tg beta +1): frac{tg beta +1}{tg beta } = frac{(tg beta +1)tg beta }{tg beta +1}=tg beta](https://tex.z-dn.net/?f=+frac%7Btg+beta+%2B1%7D%7B1%2B+frac%7B1%7D%7Btg+beta+%7D+%7D+%3D++frac%7Btg+beta+%2B1%7D%7B+frac%7Btg+beta+%7D%7Btg+beta+%7D+%2B+frac%7B1%7D%7Btg+beta+%7D+%7D%3D%28tg+beta+%2B1%29%3A+frac%7Btg+beta+%2B1%7D%7Btg+beta+%7D+%3D+frac%7B%28tg+beta+%2B1%29tg+beta+%7D%7Btg+beta+%2B1%7D%3Dtg+beta++)
tg b+1/1+ctg b, так как
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