Question

Sin^2a*cos^2b-cos^2a*sin^2b
Найдите формулу

Answer 1

$sin^2alphacos^2beta-cos^2alpha sin^2beta=sin^2alpha(1-sin^2beta)-cos^2alpha sin^2beta=\ =sin^2alpha-sin^2alpha sin^2beta-cos^2alpha sin^2beta=sin^2alpha-sin^2beta(sin^2alpha+cos^2alpha)=\ =sin^2alpha-sin^2betacdot 1=sin^2alpha-sin^2beta$