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Find all possible values of cos(x) if

 

sin(2x)=2tan(x)

 Nov 9, 2020
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Find all possible values of cos(x) if
sin(2x)=2tan(x) .

 

Hello Guest!

 

\(sin(2x)=2sin(x)cos(x)\\ \color{BrickRed}sin(2x)=2tan(x)\\ sin(x)cos(x)=tan(x)\\ tan(x)=\frac{sin(x)}{cos(x)}\\ sin(x)cos(x)=\frac{sin(x)}{cos(x)}\\ cos^2(x)=1 \)

\(cos(x)=\pm \sqrt{1}\)

\(cos_1(x)=1\\ \color{black}x_1=0\\ cos_2(x)=-1\\ \color{black}x_2=\pi\)

 

\(sin(2x)=2tan(x)\\ sin(2\cdot 0)=2\cdot tan(0)\\ 0=0\)

 

\(sin(2x)=2tan(x)\\ sin(2\cdot \pi)=2\cdot tan(\pi)\\ 0=0\)

laugh  !

 Nov 10, 2020
edited by asinus  Nov 10, 2020
edited by asinus  Nov 10, 2020

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