SOLUTION: Solve sin 4x = cos 2x

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Question 1072350: Solve sin 4x = cos 2x
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
sin 4x=2 sin 2x*cos 2x
That equals cos 2x
divide by cos 2x
2 sin 2x=1
sin 2x=(1/2)
x=pi/12
----------
check
sin pi/3 should equal cos pi/6
This is true.
Answer by ikleyn(52844)   (Show Source): You can put this solution on YOUR website!
.
sin(4x) = cos(2x)  --->  2sin(2x)*cos(2x) = cos(2x)  --->  2sin(2x)*cos(2x) - cos(2x)  = 0  --->  

cos(2x)*(2sin(2x)-1) = 0.

The last equation deploys in two independent equations:


1.  cos(2x) = 0  ---->  x = , x = ,  x =   and  x = 



2.  2sin(2x)-1 = 0  ---->  sin(2x) = ,  which implies 


    2x =   and/or   2x = .


    This, in turn, implies that the original equation has 4 (four) solutions in the interval 0 <= x < :


    x = ,  x = ,  x =   and  x = .


Answer.  In all, there are 8 solutions:  x = , x = ,  x = ,  x = ;    x = ,  x = ,  x = ,  x = .

Solved.




Plots y = sin(4x) (red) and y = cos(2x) (green)


To see more examples of solved trigonometry equations with detailed solutions, look into the lessons
    - Solving simple problems on trigonometric equations
    - Solving typical problems on trigonometric equations
    - Solving more complicated problems on trigonometric equations
    - Solving advanced problems on trigonometric equations
    - OVERVIEW of lessons on calculating trig functions and solving trig equations
in this site.


Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Trigonometry: Solved problems".


The solution by "Boreal" is wrong, since it does not cover a lot of roots.



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