Math, asked by greeshmasd3, 1 month ago

cos 45⁰/sec30⁰+cosec 30⁰​

Answers

Answered by hotshambhu1982
1

Step-by-step explanation:

here is your answer hope it would be helpful

Attachments:
Answered by BrainlySatellite51
7

\; \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}

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