PLEASE HELP, need this today

  • Thread starter Nope
  • Start date
In summary, the conversation revolved around solving the equations 2sinx+1=tanx and 2cotxsinx+cotx-2sinx-1=0, with the given domains. The conversation also mentioned using the quadratic formula and the sum to product formula. However, it was pointed out that when squaring both sides of an equation, extraneous solutions may be introduced, and it was advised to check each solution in the original equation to determine the correct solutions.
  • #1
Nope
100
0

Homework Statement


Solve 2sinx+1=tanx 0[tex]\leq[/tex]x[tex]\prec[/tex]2 pi

Homework Equations


The Attempt at a Solution


I tried to put it in this way
2sinx+1=tanx
2sinx+1=(sinx/cosx)
2sinxcosx+cosx-sinx=0
sin2x+cosx-sinx=0
I don't know what to do next, I am stuck, please help!
Thanks

Btw , can anyone show me the step for this one
2cotxsinx+cotx-2sinx-1=0 domain:0[tex]\leq[/tex]x[tex]\prec[/tex]2 pi
thanks!
 
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  • #2
What is sin2x-sinx equal to?

(Hint: Sum to product formula)
 
  • #3
rock.freak667 said:
What is sin2x-sinx equal to?

(Hint: Sum to product formula)

I haven't learn that yet...
Sin(a+b),cos(a+b)...
Sin2A=2sinAcosA, cos2A=cosx^2-sin^2...
and sinx^2+cosx^2=1 ...and other form
this is all i know
We just finished this unit today, i don't think i will learn that...

Can i square both side?
sin2x+cosx-sinx=0
(sin2x)^2=(sinx-cosx)^2
(sin2x)^2=sinx^2-2cosxsinx+cosx^2
(sin2x)^2=1-sin2x
sin2x^x+sin2x-1=0
and then use quadratic
 
Last edited:
  • #4
Nope said:
I haven't learn that yet...
Sin(a+b),cos(a+b)...
Sin2A=2sinAcosA, cos2A=cosx^2-sin^2...
and sinx^2+cosx^2=1 ...and other form
this is all i know
We just finished this unit today, i don't think i will learn that...

Can i square both side?
sin2x+cosx-sinx=0
(sin2x)^2=(sinx-cosx)^2
(sin2x)^2=sinx^2-2cosxsinx+cosx^2
(sin2x)^2=1-sin2x
sin2x^x+sin2x-1=0
and then use quadratic

yes that will work as well
 
  • #5
  • #6
What did you get when you solved this equation?
sin2x^x+sin2x-1=0
 
  • #7
Mark44 said:
What did you get when you solved this equation?
sin2x^x+sin2x-1=0

i got 4 solution,
but 2sinx+1=tanx only have 2 solution..
 
  • #8
Squaring both sides of an equation often introduces extraneous solutions that aren't solutions of the original, unsquared equation. Check each of your four solutions in your original equation. Keep only the ones that satisfy it.
 

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