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Solve for x

 

3cos (x) +2(sin)^2 (x)=0

 Mar 11, 2020
 #1
avatar+12530 
+1

Solve for x

3cos (x) +2(sin)^2 (x)=0

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 Mar 11, 2020
 #2
avatar+26396 
+2

Solve for x
3cos(x)+2sin2(x)=0

 

3cos(x)+2sin2(x)=03cos(x)=2sin2(x)|:(2)1.5cos(x)=sin2(x)

 

Substitute:

t=tan(x2)cos(x)=1t21+t2sin(x)=2t1+t2

 

1.5cos(x)=sin2(x)|cos(x)=1t21+t2, sin(x)=2t1+t21.5(1t2)(1+t2)=4t2(1+t2)21.5(1t2)=4t21+t21.5(1t2)(1+t2)=4t21.5(1t4)=4t21.5+1.5t4=4t21.5t44t21.5=0t2=4±164(1.5)(1.5)21.5t2=4±16+93t2=4±253t2=4±53t21=4+53t21=93t21=3t22=453t22=13

 

x= ?x= ?tan(x2)=t1tan(x2)=t2tan(x2)=3tan(x2)=13(the root is imaginary !)

 

tan(x2)=3tan(x2)=3tan(x2)=+3tan(x2)=3x2=arctan(3)+180kkZx2=arctan(3)+180kkZx2=60+180kkZx2=60+180kkZx=120+360kkZx=120+360kkZx=360120+360kkZx=240+360kkZ

 

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 Mar 12, 2020

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