Question

упростите выражение 1)sin⁴a+cos²a+sin²a cos²a
2)sin⁴a-cos⁴a-sin²a+cos²a
3)cos²a/1-sin²a
4)1-2sin²a/2cos²a-1

Answer 1

1)Sin⁴α + Cos²α + Sin²αCos²α = (Sin⁴α + Sin²αCos²α) + Cos²α=

= Sin²α(Sin²α + Cos²α) + Cos²α = Sin²α + Cos²α = 1

2)Sin⁴α - Cos⁴α - Sin²α + Cos²α = (Sin⁴α - Sin²α) - (Cos⁴α - Cos²α) = Sin²α(Sin²α - 1) - Cos²α(Cos²α - 1) = Sin²α * (- Cos²α) - Cos²α * (- Sin²α) =

= - Sin²αCos²α + Sin²αCos²α = 0

$3)\frac{Cos^{2}\alpha-1}{1-Sin^{2}\alpha} =\frac{-Sin^{2}\alpha}{Cos^{2}\alpha}=-tg^{2}\alpha$

$4)\frac{1-2Sin^{2}\alpha}{2Cos^{2}\alpha - 1}=\frac{Cos2\alpha }{Cos2\alpha }=1$