Can You Solve This Trigonometric Equation 2 Homework Problem?

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Homework Help Overview

The discussion revolves around a trigonometric equation involving tangent and sine functions, specifically the equation tan^2x = 2tanx*sinx. Participants are attempting to solve for the variable x.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Some participants attempt to manipulate the equation by dividing both sides by tanx, while others caution against this approach due to the possibility of tanx being zero. There is also discussion about factoring and rearranging terms to isolate variables.

Discussion Status

Participants are actively engaging with the problem, with some providing guidance on how to approach the equation without making assumptions that could lead to incorrect conclusions. There is acknowledgment of confusion regarding the steps taken, but no explicit consensus on the correct method has been reached.

Contextual Notes

There is an indication that the original poster is uncertain about their solution process and is seeking clarification on their reasoning, particularly regarding the implications of dividing by tanx.

TbbZz
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Homework Statement


tan^2x = 2tanx*sinx


Homework Equations


N/A


The Attempt at a Solution



tan^2x = 2tanx*sinx

(tan^2x)/tanx = (2tanx*sinx)/tanx

tanx = 2sinx

sinx/cosx = 2sinx

cosx = 1/2

x = [tex]pi[/tex]/3

[tex]\alpha[/tex] = [tex]pi[/tex]/3 and 5[tex]pi[/tex]/3

Not sure what I'm doing wrong.

The answer is [tex]pi[/tex]/3 and 5[tex]pi[/tex]/3 and 0, and [tex]pi[/tex]

Thanks for the assistance, I greatly appreciate it.
 
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Do not simply just divide by tanx
Bring 2tanx*sinx onto the other side and then factor out the tanx

Dividing by tanx implies that tanx is never equal to zero. Which it can be in this case.
 
TbbZz said:

Homework Statement


tan^2x = 2tanx*sinx


Homework Equations


N/A


The Attempt at a Solution



tan^2x = 2tanx*sinx

(tan^2x)/tanx = (2tanx*sinx)/tanx
Either tan2(x)/tan x= 2 tan(x) sin(x)/tan(x) or tan(x)= 0.

tanx = 2sinx

sinx/cosx = 2sinx

cosx = 1/2

x = [tex]pi[/tex]/3

[tex]\alpha[/tex] = [tex]pi[/tex]/3 and 5[tex]pi[/tex]/3

Not sure what I'm doing wrong.

The answer is [tex]pi[/tex]/3 and 5[tex]pi[/tex]/3 and 0, and [tex]pi[/tex]

Thanks for the assistance, I greatly appreciate it.
 
Thanks for the help, rock.freak667 and HallsofIvy.

I got it now.
 

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