Question

secA + tanA = x Find the value of tanA

Answer 1

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Answer 2

$\sec(A) + \tan(A) = x \: \: \: (1) \\ \\ { \sec }^{2} (A) - \tan ^{2} (A ) = 1 \\ ( \sec(A) + \tan(A) )( \sec(A) - \tan(A) ) = 1 \\ x( \sec(A) - \tan(A) ) = 1 \\ \sec(A) - \tan(A) = \frac{1}{x} \\ \text{Subtract this result from the (1) } \\ 2 \tan(A) = x - \frac{1}{x} \\ 2 \tan(A) = \frac{ {x}^{2} - 1 }{x} \\ \boxed{ \tan(A) = \frac{ {x}^{2} - 1}{2x}}$