Question

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

Answer 1

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