How do you solve for cos2x = 2 cosx sinx?

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To solve the equation cos2x = 2cosx sinx, it can be transformed using the identity 2cos(x)sin(x) = sin(2x), leading to the equivalent equation cos(2x) = sin(2x). This simplifies to tan(2x) = 1, which implies 2x = 45 + 180n for integer n. By solving for x, the values obtained are 22.5, 112.5, 202.5, and 292.5 degrees, resulting in four distinct angles within the range of 0 to 360 degrees. The discussion highlights the importance of understanding trigonometric identities and their applications in solving equations.
  • #31
I have on stupid question left:
Why do I get 4 angles instead og just 2?
Is it because tan =1?
 
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  • #32
You get 4 distinct angles because you must solve tan(2x)=1 rather than tan(x)=1
If for example, you were to solve tan(4x)=1, you would have even more distinct solutions
(You could work out how many for yourself)
 
  • #33
thanks a lot for answering all my stupid questions...
 

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