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maths homework help please!!

have this question on trig functions

(7+2cos2x)/(tan2x+3) = 3-2x

really stuck!
It's a transcendental equation. Use a numerical method. A real solution is x=0
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freddie1011
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should have mentioned but it is small angle approximations "where x is small"
oh then use

cosx=1-x^2/2 for small x
and tanx=x for small x.

you will have cos2x=1-(2x)^2/2
tan2x=2x

replace, solve a quadratic
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freddie1011
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it is a proof question asking to show how (7+2cos2x)/(tan2x+3) = 3-2x , so its not asking for x but rather to make 3-2x from (7+2cos2x)/(tan2x+3), so far ive got to 9-2x^2 / 2x+3 but dont know how to further simplify

sorry if i laid it out confusingly
you have made an error in the numerator. it should be 9-4x^2, then you have a difference of 2 squares and the answer appears
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freddie1011
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ahhhh thanks so much, got it!

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