Упростите:
[tex]\frac{1}{ctg\alpha}+\frac{cos\alpha}{1+sin\alpha}[/tex]
Ответ [tex]\frac{1}{cos\alpha}}[/tex]
Легко:1/ctga=1/(cosa/sina)=sina/cosa.
Sina/cosa+cosa/(1+sina)=((sina*(1+sina)+cos^2(a))/(cosa+cosa*sina)=(sina+sin^2(a)+cos^2(a))/(cosa*(1+sina)=(sina+1)/(cosa*(1+sina))=1/cosa.
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Answers & Comments
Легко:
1/ctga=1/(cosa/sina)=sina/cosa.
Sina/cosa+cosa/(1+sina)=((sina*(1+sina)+cos^2(a))/(cosa+cosa*sina)=(sina+sin^2(a)+cos^2(a))/(cosa*(1+sina)=(sina+1)/(cosa*(1+sina))=1/cosa.