Question

Упростите выражение (sinx +cosx)^2-1/ctgx-sinxcosx

Answer 1

$frac{(Sinx+Cosx) ^{2}- 1 }{ctgx(SinxCosx)} = frac{Sin ^{2}x + 2SinxCosx + Cos ^{2}x - 1 }{ frac{Cosx}{Sinx}(SinxCosx) } = frac{1 + 2SinxCosx - 1}{ frac{SinxCos ^{2}x }{Sinx} } =$$frac{2Sin ^{2}xCosx }{SinxCos ^{2} x} = frac{2Sinx}{Cosx} = 2tgx$