Question

The value of tan40 + 2tan10 is equal to?

A) cot50
B) cot40
C) cot10
D) None of these

Answer 1

$= > tan40 + 2tan10 \\ \\ = > tan(45 - 5) + \frac{4tan5}{1 - {tan}^{2}5 } \\ \\ = > \frac{tan45 - tan5}{1 + tan45.tan5} + \frac{4tan5}{1 - {tan}^{2}5 } \\ \\ = > \frac{1 - tan5}{1 + tan5} + \frac{4tan5}{1 - {tan}^{2} 5} \\ \\ = > \frac{1 + {tan}^{2} 5 - 2tan5 + 4tan5}{1 - {tan}^{2}5 } \\ \\ = > \frac{1 - {tan}^{2}5 + 2tan5 }{1 - {tan}^{2} 5} \\ \\ = > \frac{ {(1 + {tan}^{2}5) }^{2} }{1 - {tan}^{2}5 } \\ \\ = > \frac{1 + tan5}{1 - tan5} = \frac{cot5 + 1}{cot5 - 1} \\ \\ = > \frac{cot45.cot5 + 1}{cot45 - cot5} \\ \\ = > cot(45 - 5) \\ \\ = > cot40$
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