Przekształć wzór do najprostszej postaci:
a) sin^2 alpha+cos^2alpha+3
b) ctg alpha*sin alpha+tg beta*cos beta
c) 2sin alpha*cos alpha+(sin alpha-cos alpha)^2
d) (1+ctg^2 alpha)sin^2 alpha
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Wzory:
sin²α+cos²α=1 - jedynka trygonometryczna
ctgα=cosα/sinα
tgα=sinα/coα
(a-b)²=a²-2ab+b²
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a) sin²α+cos²α+3=
=1+3=4
---
b) ctgα*sinα+tgβ*cosβ=
=cosα/sinα * sinα + sinβ/cosβ * cosβ=
=cosα+sinα
---
c) 2sinαcosα+(sinα-cosα)²=
=2sinαcosα-2sinαcosα+sin²α+cos²α=
=1
---
d) (1+ctg²α)*sin²α=
=(1+cos²α/sin²α)*sin²α=
=sin²α+cos²α=
=1