Question

Упростить: 1-2sin^2(a)+sin^4(a)/1-2cos^2(a)+cos^4(a)

Answer 1

$\displaystyle\tt\boxed{\cos^2\alpha+\sin^2\alpha=1}\\\\ \frac{1-2\sin^2\alpha+\sin^4\alpha}{1-2\cos^2\alpha+\cos^4\alpha}=\frac{(1-\sin^2\alpha)^2}{(1-\cos^2\alpha)^2}=(\frac{\cos^2\alpha}{\sin^2\alpha})^2=(ctg^2\alpha)^2=ctg^4\alpha$