What is \(\frac{{\left( {\sin \theta + \cos \theta } \right)\left( {\t

1.	What is \(\frac{{\left( {\sin \theta + \cos \theta } \right)\left( {\tan \theta + \cot \theta } \right)}}{{\sec \theta + {\rm{cosec}}\theta }}\) equal to1). 12). 23). sin θ4). cos θ
Answer» $(\begin{array}{l} \Rightarrow \frac{{\LEFT( {\sin \THETA + \cos \theta } \right)\left( {\tan \theta + \cot \theta } \right)}}{{\sec \theta + {\rm{COSEC}}\theta }}\\ \Rightarrow \frac{{\left( {\sin \theta + \cos \theta } \right)\left( {\frac{{sin\theta }}{{cos\theta }} + \frac{{cos\theta }}{{sin\theta }}} \right)}}{{\frac{1}{{cos\theta }} + \frac{1}{{sin\theta }}}}\\ \Rightarrow \frac{{\frac{{\left( {\sin \theta + \cos \theta } \right)\left( {(SI{n^2}\theta + co{s^2}\theta } \right)}}{{sin\theta cos\theta }})}}{{\frac{{sin\theta + cos\theta }}{{sin\theta cos\theta }}}} \end{array})$ ? sin²θ + cos²θ = 1 $(\Rightarrow {\rm{\;}}\frac{{\left( {\sin \theta + \cos \theta } \right)}}{{\sin \theta + \cos \theta }} = {\rm{\;}}1)$

What is $\frac{{\left( {\sin \theta + \cos \theta } \right)\left( {\tan \theta + \cot \theta } \right)}}{{\sec \theta + {\rm{cosec}}\theta }}$ equal to1). 12). 23). sin θ4). cos θ

Answer»

$(\begin{array}{l} \Rightarrow \frac{{\LEFT( {\sin \THETA + \cos \theta } \right)\left( {\tan \theta + \cot \theta } \right)}}{{\sec \theta + {\rm{COSEC}}\theta }}\\ \Rightarrow \frac{{\left( {\sin \theta + \cos \theta } \right)\left( {\frac{{sin\theta }}{{cos\theta }} + \frac{{cos\theta }}{{sin\theta }}} \right)}}{{\frac{1}{{cos\theta }} + \frac{1}{{sin\theta }}}}\\ \Rightarrow \frac{{\frac{{\left( {\sin \theta + \cos \theta } \right)\left( {(SI{n^2}\theta + co{s^2}\theta } \right)}}{{sin\theta cos\theta }})}}{{\frac{{sin\theta + cos\theta }}{{sin\theta cos\theta }}}} \end{array})$

? sin²θ + cos²θ = 1

$(\Rightarrow {\rm{\;}}\frac{{\left( {\sin \theta + \cos \theta } \right)}}{{\sin \theta + \cos \theta }} = {\rm{\;}}1)$

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