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July 2022
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Известно, что sinα + cosα = p
Найдите: sinα - cosα
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армения20171
Sina+cosa=p
(sina+cosa)²=p²
sin²a+2sina*cosa+cos²a=p²
1+2sina*cosa=p²
2sina*cosa=p²-1
sina-cosa=?
(sina-cosa)²=1-2sina*cosa=1-p²+1=2-p²
sina-cosa=√(2-p²); p€[-1;1]
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Answers & Comments
(sina+cosa)²=p²
sin²a+2sina*cosa+cos²a=p²
1+2sina*cosa=p²
2sina*cosa=p²-1
sina-cosa=?
(sina-cosa)²=1-2sina*cosa=1-p²+1=2-p²
sina-cosa=√(2-p²); p€[-1;1]