1-ctg^2a = -cos2a/sin^2a докажите тождество

[tex]1-ctg^{2} \alpha =\frac{-cos2 \alpha}{sin^{2} \alpha}\\1-ctg^{2} \alpha= \frac{-2cos^{2} \alpha +1 }{sin^{2} \alpha }\\1-ctg^{2} \alpha= -2ctg^{2} \alpha + \frac{1}{sin^{2} \alpha }\\1-ctg^{2} \alpha = -2ctg^{2} \alpha +(1+ctg^{2} \alpha )\\1-ctg^{2} \alpha =1-ctg^{2} \alpha [/tex]