Question

If a+b+c=180 degree then value oof tan a/2tanb/2 is

Answer 1

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we have to Find Tana/2 × Tanb/2 ?

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$a + b + c = 180 = \pi \\ \\ (a + b) = (\pi - c) \\ \\ ( \frac{a + b}{2} ) = ( \frac{\pi}{2} - \frac{c}{2} ) \\ \\ tan( \frac{a}{2} + \frac{b}{2} ) = cot \frac{c}{2} \\ \\ \\ ( \frac{tan \frac{a}{2} + tan \frac{b}{2} }{1 - tan \frac{a}{2} \times tan \frac{b}{2} } ) = \frac{1}{tan \frac{c}{2} } \\ \\ (tan \frac{a}{2} \times tan \frac{b}{2} ) = tan \frac{c}{2} (tan \frac{a}{2} + tan \frac{b}{2} ) + 1$

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