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Question
solve equation for x where 0<= x <2pi
cos 2x cos x - sin 2x sin x = -1
Hi Nanci,
This one can be very difficult if you treat it one way, but very simple if you take another approach. Let's try the second way:
Think of 2x as A and x as B, then the left is
cos A cos B - sin A sin B
which is the formula for cos (A + B):
So, cos(2x + x) = -1 ----> cos 3x = -1
Because of the 3x, go 3 rotations:
3x = pi, 3pi, 5pi
so x = pi/3, pi, 5pi/3.
Trying anything else, like double angle formulas on cosine and sine, make the problem unmanageable
Steve
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| Comment | Thanks so much. I tried to solve with double angle identies and was getting no where. I even went back to the instructor and she had difficulties and thought maybe she had an error in the question. Thanks again she will like the answer. | ||
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Answers by Expert:
Steve Holleran
Expertise
I can help with all math questions from basic math to Calculus. Whether it`s consumer questions, or questions from high school or college students, I have probably dealt with it at some time in my career.
Experience
33 years teaching experience in NJ public schools
Education/Credentials
B.S. Mathematics : Wake Forest University 1972
M.S. Mathematics : Monmouth University 1981
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