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pablos28spainzd

pablos28spainzd

Answered question

2022-07-09

The number of solutions to cos 2 x = cos 2 x .
How can one quickly find out the number of solutions to
cos 2 x = cos 2 x ,       0 x 2 π   ?
I rewrote the equation as
cos 2 x = cos 2 x sin 2 x sin 2 x = 0 sin x = 0.
So, the equation sin x = 0 has roots on 0 , π and 2 π. So the answer should be 3. Is this an acceptable and all correct reasoning or can I improve on any detail? Is the answer correct?

Answer & Explanation

Ashley Parks

Ashley Parks

Beginner2022-07-10Added 11 answers

Yes, this is an excellent example of using the double-angle formula for the cosine. There's nothing wrong with it, and it seems (to me) to be the fastest method of solving.

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