Question

Помогите упростить пожалуйста

Answer 1

$\frac{tg\alpha}{cos\alpha sin^3\alpha+sin\alpha cos^3\alpha}-1=\frac{tg\alpha}{cos\alpha sin\alpha(sin^2\alpha+cos^2\alpha)}-1=\frac{\frac{sin\alpha}{cos\alpha}}{cos\alpha sin\alpha}-1=\\\\\frac{\frac{sin\alpha}{cos\alpha}}{cos\alpha sin\alpha}-1=\frac{1}{cos^2\alpha}-1=\frac{1-cos^2\alpha}{cos^2\alpha}=\frac{sin^2\alpha}{cos^2\alpha}=tg^2\alpha$