Question

pls answer fast,.........​

Answer 1

SOLUTION

We have,

$m = \frac{</strong><strong>cosA</strong><strong>}{</strong><strong>cosB</strong><strong>} \: \: \: n = \frac{</strong><strong>cosA</strong><strong>}{</strong><strong>sinB</strong><strong>} \\ \\ now \\ </strong><strong>L</strong><strong>.</strong><strong>H</strong><strong>.</strong><strong>S</strong><strong> = ( {m}^{2} + {n}^{2} ) {cos}^{2} </strong><strong>B</strong><strong> \\ \\ = > ( \frac{ {cos}^{2}</strong><strong>A</strong><strong> }{ {cos}^{2} </strong><strong>A</strong><strong>} + \frac{cos {}^{2} </strong><strong>A</strong><strong>}{ {sin}^{2} </strong><strong>B</strong><strong>} )\times {cos}^{2} </strong><strong>B</strong><strong> \\ \\ = > ( \frac{ {cos}^{2} </strong><strong>A</strong><strong>. {sin}^{2}</strong><strong>B</strong><strong> + {cos}^{2}</strong><strong>A</strong><strong>. {cos}^{2} </strong><strong>B</strong><strong> }{ {cos {}^{} }^{2} </strong><strong>B</strong><strong>.sin {}^{2}</strong><strong>B</strong><strong> } ) \times {cos}^{2} </strong><strong>B</strong><strong>\\ \\ = > \frac{ {cos}^{2}</strong><strong>A</strong><strong>( {sin}^{2} </strong><strong>B</strong><strong>+ {cos}^{2}</strong><strong>B</strong><strong>) }{ {sin}^{2} </strong><strong>B</strong><strong>} \\ \\ = > \frac{ {cos}^{2}</strong><strong>A</strong><strong>}{sin {}^{2} </strong><strong>B</strong><strong>} = {n}^{2}$

R.H.S

hope it helps ☺️