Question

If tan2A =24/7 then show that tanA=3/4.

Answer 1

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$\tan(2a) \: = \frac{24}{7} \\ \frac{2\tan(a) }{1 - { \tan(a) }^{2} } = \frac{24}{7} \\ 12 { \tan(a) }^{2} + 7 \tan(a) - 12 = 0 \\ \tan(a) = \frac{3}{4} and \: - \frac{4}{3}$

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