Question

secx= x+1/x find secx.tanx

Answer 1

♧♧HERE IS YOUR ANSWER♧♧

Given :

$sec \: x = \frac{x + 1}{x} \\ \\ squaring \: \: we \: \: get \\ \\ {sec}^{2} x = \frac{ {(x + 1)}^{2} }{ {x}^{2} } \\ \\ = > \: \: 1 + {tan}^{2} x = \frac{ {x}^{2} + 2x + 1}{ {x}^{2} } \\ \\( since \: \: {sec}^{2} x - {tan}^{2} x = 1) \\ \\ = > {tan}^{2} x = \frac{ {x}^{2} + 2x + 1 }{ {x}^{2} } - 1 \\ \\ = > {tan}^{2} x = \frac{ {x}^{2} + 2x + 1 - {x}^{2} }{ {x}^{2} } \\ \\ = > {tan}^{2} x = \frac{2x + 1}{ {x}^{2} }$

Now,

${sec}^{2} x \: {tan}^{2} x \\ \\ = ({ \frac{x + 1}{x} })^{2} \times (\frac{2x + 1}{ {x}^{2} } ) \\ \\ = \frac{ {(x + 1)}^{2} (2x + 1)}{ {x}^{4} }$

Then,

$secx \: tanx = \frac{(x + 1) \sqrt{2x + 1} }{ {x}^{2} }$

♧♧HOPE THIS HELPS YOU♧♧