Question

Упростить: $frac{1-4sin^{2}t cos^{2}t}{cos^{2}t-sin^{2}t}$

Answer 1

$frac{1-4sin^2t*cos^2t}{cos^2t-sin^2t} = frac{1-(2sint*cost)^2}{cos^2t-sin^2t} = frac{1-(sin2t)^2}{cos2t} = frac{cos^22t}{cos2t} =cos2t$

$cos2t=cos^2t-sin^2t$
$sin2t=2sint*cost$