Question

if tan X + tan Y =5 and tan X × tan Y =1/2 then prove that cot(X+Y) =10.​

Answer 1

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As per given

$\tan(x) + \tan(y) = 5 \\ \\ \tan(x) \tan(y) = \frac{1}{2}$

So

$= > \cot(x + y) \\ \\ = > \frac{1 }{ \tan(x + y) } \\ \\ = > \frac{1 - \tan(x) \tan(y) }{ \tan(x) + \tan(y) } \\ \\ = > \frac{1 - \frac{1}{2} }{5} \\ \\ = > \frac{ \frac{2 - 1}{2} }{5} \\ \\ = > \frac{ \frac{1}{2} }{5} \\ \\ = > \frac{1}{10}$

Note

There is need of correction in question

• That is tan(x+y) not cot(x+y)

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