Question

Cos 45°/sec30°+cosec 30 °​

Answer 1

Answer:

Given, cos 45/(sec 30 + cosec 30)

= (1/√2)/(2/√3 + 2) {since cos 45 = 1/√2, sec 30 = 2/√3, cosec 30 = 2}

= (1/√2)/{(2 + 2√3)/√3}

= (√3/√2)/(2 + 2√3)

= √3/{√2*(2 + 2√3)}

= √3/(2√2 + 2√3*√2)

= √3/(2√2 + 2√6)

So, cos 45/(sec 30 + cosec 30) = √3/(2√2 + 2√6)

HOPE THAT IT WAS HELPFUL!!!!

MARK IT THE BRAINLIEST IF IT REALLY WAS!!!!

Answer 2

$\; \star \; {\underline{\boxed{\pmb{\orange{\frak{ To Evaluate\; :- }}}}}}$

$\sf \longmapsto{ \dfrac{ \cos45 \degree }{ \sec30 \degree + \cosec30 \degree } }$

$\begin{gathered} \\ \\ \end{gathered}$

$\; \star \; {\underline{\boxed{\pmb{\purple{\frak{ \; SolutioN \; :- }}}}}}$

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { \dfrac{ \cos45 \degree }{ \sec30 \degree + \cosec30 \degree} } \\ \\ \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { \dfrac{ \dfrac{1}{ \sqrt{2} } }{ \dfrac{2}{ \sqrt{3} } + 2 } } \\ \\ \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { \dfrac{ \dfrac{1}{ \sqrt{2} } }{ \dfrac{2 +2 \sqrt{3} }{ \sqrt{3} } } } \\ \\ \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { \dfrac{1}{ \sqrt{2} } \times { \dfrac{\sqrt{3} }{ 2 + \sqrt{3} } } } \\ \\ \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { { \dfrac{\sqrt{3} }{ 2 \sqrt{} 2 +2 \sqrt{6} } } } \\ \\ \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { { \dfrac{\sqrt{3} }{ 2 \sqrt{} 2 +2 \sqrt{6} } \times \dfrac{2 \sqrt{2} - 2 \sqrt{6} }{2 \sqrt{2} - 2 \sqrt{6} }}} \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { { \dfrac{\sqrt{3} ( 2 \sqrt{} 2 - 2 \sqrt{6})}{ (2 \sqrt{} 2) {}^{2} - (2 \sqrt{6} ) {}^{2} } }} \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { { \dfrac{2\sqrt{3} ( \sqrt{} 2 - \sqrt{6})}{8 - 24 } }} \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { { \dfrac{2\sqrt{3} ( \sqrt{} 2 - \sqrt{6})}{ - 16} }} \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { { \dfrac{ \cancel{2} ( \sqrt{} 6 - \sqrt{18})}{ \cancel{- 16}} }} \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { { \dfrac{ ( \sqrt{} 6 - \sqrt{18})}{ {- 8}} }} \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { { \dfrac{ - ( \sqrt{} 18 - \sqrt{6} )} { {- 8}} }} \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { { \dfrac{ \cancel{ -} ( \sqrt{} 18 - \sqrt{6} )} { { \cancel{-} 8}} }} \end{gathered}$

$\begin{gathered} \; \longmapsto \; \sf { { \dfrac{ ( \sqrt{} 18 - \sqrt{6} )} { { 8}} }} \end{gathered}$

$\begin{gathered} \\ \\ \end{gathered}$

$\begin{gathered} \; \longmapsto \; {\underline{\boxed{\red{\sf { \dfrac{ \cos45 \degree }{ \sec30 \degree + \cosec30 \degree} = \dfrac{ ( \sqrt{} 18 - \sqrt{6} )} { { 8}}}}}}} \; \bigstar \\ \\ \end{gathered}$

$\begin{gathered} \\ {\underline{\rule{300pt}{9pt}}} \end{gathered}$