Question

1-sin^2a(1+ctg^2a) ​

Answer 1

$1-\sin^2a(1+\mathrm{ctg}\,^2a)=1-\sin^2a-\sin^2a\cdot\mathrm{ctg}\,^2a=$

$=1-\sin^2a-\sin^2a\cdot\dfrac{\cos^2a}{\sin^2a} =1-\sin^2a-\cos^2a=$

$=1-(\sin^2a+\cos^2a)=1-1=0$