Question

if sec A + tan A = a , find the value of sec A and tan A​

Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: find : \\ values \: of \: sec \: A \: and \: tan \: A \\ (in \: terms \: of \: a) \\ \\ so \: here \\ sec \: A + tan \: A = a \\∴ \: \: sec \: A = a - tan \: A \\ \\ we \: know \: that \\ 1 + tan {}^{2} A = sec {}^{2} A \\ \\ = (a - tan \: A) {}^{2} \: \: \: \: \: \: \\ \\ 1 + tan {}^{2} A= a {}^{2} + tan {}^{2} A - 2a.tan \: A \\ \\ 2a.tan \: A = a {}^{2} - 1 \\ \\ tan \: A = \frac{a {}^{2} - 1 }{2a} \\ \\ thus \: then \\ sec \: A = a - tan \: A \\ \\ = a - ( \frac{a {}^{2} - 1}{2a} \: ) \\ \\ = \frac{2a {}^{2} - (a {}^{2} - 1) }{2a} \\ \\ = \frac{a {}^{2} + 1}{2a} \\ \\ sec \: A = \frac{a {}^{2} + 1}{2a}$