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Prove It · #3 July 3rd, 2009, 08:50 AM

Quote:

Originally Posted by dhiab

1 ) Solve in R this equation: $\cos 2x + 2\sin x\cos x = 0$ ( let:tan x= t)
2 )Deduct the values of :
$\cos \left( {\frac{\pi }{8}} \right),\cos \left( {\frac{{3\pi }}{8}} \right),\sin \left( {\frac{\pi }{8}} \right),\sin \left( {\frac{{3\pi }}{8}} \right)$

$2\sin{x}\cos{x} = \sin{(2x)}$ .

So if $\cos{(2x)} + 2\sin{x}\cos{x} = 0$

$\cos{(2x)} + \sin{(2x)} = 0$

$\cos{(2x)} = -\sin{(2x)}$

$1 = -\frac{\sin{(2x)}}{\cos{(2x)}}$

$-\tan{(2x)} = 1$

$2x = \left\{\frac{\pi}{4}, \frac{5\pi}{4}\right\} + 2\pi n$ , where $n \in \mathbf{Z}$

$x = \frac{1}{2}\left[\left\{\frac{\pi}{4}, \frac{5\pi}{4}\right\} + 2\pi n\right]$

$x = \left\{\frac{\pi}{8}, \frac{5\pi}{8}\right\} + \pi n$ , where $n \in \mathbf{Z}$ .

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