докажите тождество: sin\1+cos = 1-cos\sin. Created by katewatson320. algebra-ru

докажите тождество: sin\1+cos = 1-cos\sin...

katewatson320 @katewatson320

August 2022 1 15 Report

докажите тождество: sin\1+cos = 1-cos\sin

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Universalka

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$\frac{Sin \alpha }{1+Cos \alpha }- \frac{1-Cos \alpha }{Sin \alpha }= \frac{Sin ^{2} \alpha - (1-Cos \alpha )(1+Cos \alpha ) }{Sin \alpha (1+Cos \alpha )} = \frac{Sin ^{2} \alpha -1+Cos ^{2} \alpha }{Sin \alpha (1+Cos \alpha )} =$ $\frac{-Cos ^{2} \alpha +Cos ^{2} \alpha }{Sin \alpha (1+Cos \alpha )}= \frac{0}{Sin \alpha (1+Cos \alpha )}= 0$
Если разность левой и правой частей равна нулю, то левая часть равна правой. Тождество доказано.

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