Question

установите соответствия

Answer 1

$2cos^2a=1+cos2a\\\\cos^4a-sin^4a=(cos^2a-sin^2a)(\underbrace {cos^2a+sin^2a}_{1})=cos^2a-sin^2a=cos2a\\\\2sin^2a=1-cos2a\\\\2cos^2a-cos2a=2cos^2a-(cos^2a-sin^2a)=cos^2a+sin^2a=1\\\\2cos^22a-cos2a=1+cos4a-cos2a\\\\(cosa-sina)^2=cos^2a+sin^2a-2\, sina\, cosa=1-sin2a\\\\\\\star \; \; 1+sin2a=sin^2a+cos^2a+2\, sina\cdot cosa=(sina+cosa)^2\; \; \star$