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I got stuck on solving the following equation. I try all the identities, but hopeless. Do you have any suggestion?

$$(3x + \sin x) \cos x = -3, \quad\pi/2 \leq x \leq \pi$$ Solve for $x$.

Please don't tell me to use the calculator!

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    Solutions do not appear to have a closed-form. If the only thing we can know about the zeros are approximations, then what do you want us to tell you?2012-04-04
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    Why not use the calculator? There is almost certainly no "closed form" solution. So if one wants some kind of answer, one will have to use a numeical method of some kind. There is a unique solution in your interval, not far from $x=2$.2012-04-04
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    By chance, is the equation supposed to be $(3x+\sin x)\cos x=-3\pi$? Did you encounter this problem in a trig course, a calculus course, or somewhere different?2012-04-04

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