(Klasa 2 technikum)
Udowodnij tożsamość trygonometryczną:
a) cosα*sin²α+cos³α=cosα
b) 1-2sinα*cosα=(sinα-cosα)²
c) cos²α+tg²α*cos²α=1
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a)
cosα*sin²α+cos³α=cosα
L=cosα(sin²α+cos²α)=cosα*1=cosα
P=cosα
L=P
b)
1-2sinα*cosα=(sinα-cosα)²
L=1-2sinα*cosα
P=sin²α+cos²α-2sinαcosα=1-2sinα*cosα
L=P
c)
cos²α+tg²α*cos²α=1
L=cos²α+tg²α*cos²α=cos²α+(sin²α/cos²α)*cos²α=cos²α+sin²α=1
P=1
L=P