Question

If tan A = 5/6 and tan B=1/11 .
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prove that A + B = 45°​

Answer 1

Answer:

$tan(a + b) = \frac{tan \: a +tan \: b}{1 + tan \: a \: tanb} \\ tan(a + b) = \frac{ \frac{5}{6} + \frac{1}{11} }{1 + \frac{5}{6} \times \frac{1}{11} } \\ tan(a + b) = \frac{ \frac{61}{66} }{1 + \frac{5}{66} } \\ tan(a + b) = \frac{ \frac{61}{66} }{ \frac{61}{66} } \\ tan(a + b) = 1 \\ \\ but \: tan \: 45 = 1 \\ \\ therefore \\ a + b = 45$

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