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Sagot :
Step-by-step explanation:
[tex] \tan( \frac{x}{2} ) = \frac{ \sin(x) }{1 + \cos(x) } [/tex]
[tex] \tan( \frac{x}{2} ) = \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } [/tex]
So we have
[tex] \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } = \frac{ \sin(x) }{ \sqrt{1 + \cos(x) } } [/tex]
Next, we then rationalize the numerator so we get
[tex] \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } \frac{ \sqrt{1 + \cos(x) } }{1 + \cos(x) } = \frac{ \sin(x) }{ {1 + \cos(x) } } [/tex]
The denominator should be square root so to let you know .
So know we ahev
[tex] \frac{ \sqrt{1 - \cos {}^{2} (x) } }{1 + \cos(x) } = \frac{ \sin(x) }{1 + \cos(x) } [/tex]
[tex] \frac{ \sqrt{ \sin {}^{2} (x) } }{1 + \cos(x) } = \frac{ \sin(x) }{ {1 + \cos(x) } } [/tex]
[tex] \frac{ \sin(x) }{1 + \cos(x) } = \frac{ \sin(x) ) }{1 + \cos(x) } [/tex]
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