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Объяснение:
2*2sinxcosx-sinxcosx=cosx^2-sinx^2
4sinxcosx-sinxcosx=cosx^2-sinx^2
3sinxcosx-sinxcosx-cosx^2+sinx^2=0
3sinxcosx-(1-sinx^2)+sinx^2=0
3sinxcosx-1+sinx^2+sinx^2=0
3sinxcosx-1+2sinx^2=0
3sinxcosx+2sinx^2=1
3sinxcosx+2sinx^2=sinx^2+cosx^2
3sinxcosx+2sinx^2-sinx^2-cosx^2=0
3sinxcosx+sinx^2-cosx^2=0
3tanx+tanx^2-1=0
3t+t^2-1=0
t=
⊆![x=\left \{ {{arctan(\frac{-3+\sqrt{13} }{2} )+k\pi } \atop {-arctan\frac{3+\sqrt13}{2}}+k\pi } \right.](/tpl/images/1523/9775/909b5.png)
Объяснение:
2*2sinxcosx-sinxcosx=cosx^2-sinx^2
4sinxcosx-sinxcosx=cosx^2-sinx^2
3sinxcosx-sinxcosx-cosx^2+sinx^2=0
3sinxcosx-(1-sinx^2)+sinx^2=0
3sinxcosx-1+sinx^2+sinx^2=0
3sinxcosx-1+2sinx^2=0
3sinxcosx+2sinx^2=1
3sinxcosx+2sinx^2=sinx^2+cosx^2
3sinxcosx+2sinx^2-sinx^2-cosx^2=0
3sinxcosx+sinx^2-cosx^2=0
3tanx+tanx^2-1=0
3t+t^2-1=0
t=![\frac{-3+\sqrt{13} }{2}](/tpl/images/1523/9775/b597d.png)
t=![\frac{-3-\sqrt{13} }{2}](/tpl/images/1523/9775/01dce.png)