tex]...

qaz2016 @qaz2016

December 2021 1 16 Report

Упростите выражения:
[tex]a) tg \beta *ctg \beta - sin^2 \alpha

b) ctg\alpha /tg \alpha + sin^2 \alpha + cos^2 \alpha

c) 1 + tg\alpha/1 + ctg \alpha [/tex]

Answers & Comments

Freakazoid

Verified answer

$a) \; tg \beta ctg \beta -sin^2 \alpha =1-sin^2a=cos^2a;\\b) \; \frac{ctg \alpha }{tg \alpha }+sin^2a+cos^2a=\frac{cosa}{sina}:\frac{sina}{cosa}+1=ctg^2a+1=\frac{1}{sin^2a};\\
c)\; \frac{1+tga}{1+ctga}=\frac{\frac{cosa+sina}{cosa}}{\frac{sina+cosa}{sina}}=\frac{sina+cosa}{cosa}*\frac{sina}{sina+cosa}=tga.$

Использованы основные тригонометрические тождества:
$sin^2a+cos^2a=1;\\tga*ctga=1.$

3 votes Thanks 3

Answers & Comments

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