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| trig equation https://forumdematematica.org/viewtopic.php?f=23&t=337 |
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| Autor: | kinu [ 27 abr 2012, 17:04 ] |
| Título da Pergunta: | trig equation |
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| Autor: | kinu [ 18 mai 2012, 15:38 ] |
| Título da Pergunta: | Re: trig equation |
Thanks friends i have got it If \(Ax^2+Bx+C=0\) has more then Two Roots, Then It will become an Identity Which is True for all Real \(x\) So \(A=B=C=0\) Now here \(\left(a-\sin \theta\right)\alpha^2+b\alpha+\left(c+\cos \theta\right) = 0\) Similarly \(\left(a-\sin \theta\right)\beta^2+b\beta+\left(c+\cos \theta\right) = 0\) and \(\left(a-\sin \theta\right)\gamma^2+b\gamma+\left(c+\cos \theta\right) = 0\) Now again If Given equation has more the 2 roots, then \(a-\sin \theta = b = c+\cos \theta = 0\) So \(a = \sin \theta\) and \(b = 0\) and \(c = -\cos \theta\) Now \(a+b+c = 1\) So \(\sin \theta-\cos \theta = 1\Leftrightarrow \sin \left(\theta -\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} = \sin \left(\frac{\pi}{4}\right)\) So \(\theta = \frac{\pi}{2}\;\;,\pi\) |
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