Mathematics, 27.08.2019 09:20 xojade
Solve the equation on the interval [0,2π). cos^4x=cos^4xcscx
Answers: 1
![\bf cos^4(x)=cos^4(x)csc(x)\\\\ -----------------------------\\\\ cos^4(x)=cos^4(x)\cfrac{1}{sin(x)}\implies cos^4(x)=\cfrac{cos^4(x)}{sin(x)} \\\\\\ cos^4(x)sin(x)=cos^4(x)\implies cos^4(x)sin(x)-cos^4(x)=0 \\\\\\ cos^4(x)[sin(x)-1]=0\to \begin{cases} cos^4(x)=0\to x=cos^{-1}(0)\\ ----------\\ sin(x)-1=0\\ sin(x)=1\to x=sin^{-1}(1) \end{cases}](/tpl/images/0202/0138/f8a4b.png)
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Solve the equation on the interval [0,2π). cos^4x=cos^4xcscx...
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