Доказать тождество (1-sina)(1+sina)=cos^2a. Created by hollyananas. matematika-ru

Доказать тождество (1-sina)(1+sina)=cos^2a...

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$(1-sina)(1+sina)=cos^2a \\ 1^2-sin^2\alpha=cos^2\alpha \\ \boxed{cos^2\alpha+sin^2\alpha=1} \Rightarrow \boxed{cos^2\alpha=1-sin^2\alpha}$
$cos^2\alpha=cos^2\alpha$ - доказано.

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1Parviz

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Решение:
(1-sina)(1+sina)=cos^2a
(1-sina)(1+sina)=1²-sin²a=1-sin²a-это даёт формулу =cos²a т.е.:
cos²a=cos²a или cos^2a=cos^2a
Тождество доказано.

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