Question

Докажите
$cos2a=1-2sin^2a$

Answer 1

cos2a=cos²a-sin²a=1-sin²a-sin²a=1-2sin²a
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sin²a+cos²a=1

Answer 2

$cos(a+a)=1-2sin^2a \\cosa*cosa-sina*sina=1-2sin^2a \\cos^2a-sin^2a=1-2sin^2a \\(1-sin^2a)-sin^2a=1-2sin^2a \\1-2sin^2a=1-2sin^2a$