Question

упростить выражение (sin t +cos t )^2 /( 1 +2 sin t cos t )

Answer 1

= (sin^2(t) +2*sint*cost+cos^2(t)) /( 1 +2 sin t cos t )=
=(1+2*sint*cost)/(1+2*sint*cost)=1

Answer 2

$frac{(sin t + cos t)^{2} }{1+2sin t cos t} = frac{sin^{2}t+2sin tcos t+cos^{2}t}{1+2sin tcos t}= frac{1+2sin tcos t}{1+2sin t cos t}=1$