Question

sec a + tan a = x then find the value of sec a ​

Answer 1

Explanation:

$\tt We\:know\:the\: identity \\ \\ \tt 1 + {tan}^{2}A = {sec}^{2}A \\ \\ \tt \longrightarrow {sec}^{2}A - {tan}^{2}A = 1 \\ \\ \tt \longrightarrow ( secA + tanA )( secA - tanA ) = 1 \\ \\ \tt \longrightarrow secA - tanA = \frac{1}{secA + tanA } \\ \\ \tt So \: if \:secA + tanA = x \: then \: secA - tanA = \frac{1}{x} \\ \\ \tt Adding\:above\:two\:equations \\ \\ \tt \longrightarrow 2secA = x + \frac{1}{x} \\ \\ \tt \longrightarrow 2secA = \frac{{x}^{2}+1}{x} \\ \\ \tt \longrightarrow \boxed{\bold{\red{\tt secA = \frac{{x}^{2}+1}{2x} }}}$

❣️NIRANJAN45❣️

Answer 2

Answer:

Sec a = x² + 1/2x.

Hope it will help you...