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Solve cos2xsinx=1

  • #1

Homework Statement


Simplify AND Solve for X
cos2xsinx=1


Homework Equations


The triples, doubles


The Attempt at a Solution


cos2xsinx=1
(cos^2x-sin^2x)(sinx)=1
(-1x)(sinx)=1
-sinx=1
sinx= -1
?


..

:-/

Help.. :)
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618


The maximum absolute value of cos(2x) and sin(x) is 1. So the only way you can solve that is if cos(2x)=1 AND sin(x)=1 or cos(2x)=(-1) AND sin(x)=(-1). Is either of those possible? If so which one?
 
  • #3


I have no idea may i have another clue
 
  • #4


anyone?
 
  • #5
Dick
Science Advisor
Homework Helper
26,258
618


I have no idea may i have another clue
Graph cos(2x) and sin(x) on [0,2pi]. Or do this cos^2(x)-sin^2(x)=1-2*sin^2(x). So you have (1-2*sin^2(x))*sin(x)=1. If sin(x)=u then you have (1-2*u^2)*u=1. That's a cubic equation for u. Can you find the real root?
 
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