trygonometria
Darek: Uprościć wyrażenie:
sin2(α+β)−sin2(α−β)
30 lis 21:21
Mila:
Np. tak:
[sin(α+β)−sin(α−β)]*[sin(α+β)+sin(α−β)]=
| | α+β+α−β | | α+β−α+β | | α+β+α−β | | α+β−α+β | |
=2*sin |
| *cos |
| *2*cos |
| *sin |
| = |
| | 2 | | 2 | | 2 | | 2 | |
=2*2sinα*cosβ*cosα*sinβ=
=(2*sinα*cosα)*(2sinβ*cosβ)=
=
sin(2α)*sin(2β)
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30 lis 21:56