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Old July 3rd, 2009, 08:50 AM
Prove It Prove It is offline
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Quote:
Originally Posted by dhiab View Post
1 ) Solve in R this equation: ( let:tan x= t)
2 )Deduct the values of :
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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