Noon Academy
Prove:
contexto.140
3 years ago
![\[{{\left( \mathbf{sin}\text{ }\mathbf{A}\text{ }+\text{ }\mathbf{cosec}\text{ }\mathbf{A} \right)}^{\mathbf{2}}}~+\text{ }{{\left( \mathbf{cos}\text{ }\mathbf{A}\text{ }+\text{ }\mathbf{sec}\text{ }\mathbf{A} \right)}^{\mathbf{2}}}~=\text{ }\mathbf{7}\text{ }+\text{ }\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}~\mathbf{A}\text{ }+\text{ }\mathbf{co}{{\mathbf{t}}^{\mathbf{2}}}~\mathbf{A}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-40467e8881639664e2fc64c4854e5482_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} LHS, \\ {{\left( sin\text{ }A\text{ }+\text{ }cosec\text{ }A \right)}^{2}}~+\text{ }{{\left( cos\text{ }A\text{ }+\text{ }sec\text{ }A \right)}^{2}} \\ =\text{ }si{{n}^{2}}~A\text{ }+\text{ }cose{{c}^{2}}~A\text{ }+\text{ }2\text{ }sin\text{ }A\text{ }cosec\text{ }A\text{ }+\text{ }co{{s}^{2}}~A\text{ }+\text{ }se{{c}^{2}}~A\text{ }+\text{ }2cos\text{ }A\text{ }sec\text{ }A \\ =\text{ }\left( si{{n}^{2}}~A\text{ }+\text{ }co{{s}^{2}}~A\text{ } \right)\text{ }+\text{ }cose{{c}^{2}}~A\text{ }+\text{ }se{{c}^{2}}~A\text{ }+\text{ }2\text{ }+\text{ }2 \\ =\text{ }1\text{ }+\text{ }cose{{c}^{2}}~A\text{ }+\text{ }se{{c}^{2}}~A\text{ }+\text{ }4 \\ =\text{ }5\text{ }+\text{ }\left( 1\text{ }+\text{ }co{{t}^{2}}~A \right)\text{ }+\text{ }\left( 1\text{ }+\text{ }ta{{n}^{2}}~A \right) \\ =\text{ }7\text{ }+\text{ }ta{{n}^{2}}~A\text{ }+\text{ }co{{t}^{2}}~A\text{ }=\text{ }RHS \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6d72bbb1e52b46ca55e8d072fba3f5da_l3.png "Rendered by QuickLaTeX.com")
