(cos A/1+sin A )+(1+sin A/cosA)

1.	(cos A/1+sin A )+(1+sin A/cosA)
Answer» ANSWER: $\huge\rm{\underline{\underline{Given\rightarrow}}}$ $\mathrm\green{\dfrac{(CosA)}{(1+SinA)}+\dfrac{(1+SinA)}{(CosA)}}$ $\huge\rm{\underline{\underline{To\:Perform\rightarrow}}}$ $\mathrm\purple{\rightarrow{Simplification\:of\:the\:equation.}}$ $\huge\rm{\underline{\underline{Answer\rightarrow}}}$ $\mathrm\blue{\rightarrow{\dfrac{(CosA)}{(1+SinA)}+\dfrac{(1+SinA)}{(CosA)}}}$ $\mathrm\blue{\rightarrow{\dfrac{(CosA.CosA)}{(1+SinA.CosA)}+\dfrac{(1+SinA.1+SinA)}{(CosA.1+SinA)}}}$ $\mathrm\blue{\rightarrow{\dfrac{(Cos^2A)}{(1+SinA.CosA)}+\dfrac{(1+SinA)^2}{(CosA.1+SinA)}}}$ $\mathrm\blue{\rightarrow{\dfrac{Cos^2A+(1+SinA)^2}{(CosA.1+SinA)}}}$ $\mathrm\blue{\rightarrow{\dfrac{Cos^2A+1+Sin^2A+2SinA)}{(CosA.1+SinA)}}}$ $\mathrm\blue{\rightarrow{\dfrac{Cos^2A+Sin^2A+2SinA+1}{(CosA.1+SinA)}}}$ $\mathrm\blue{\rightarrow{\dfrac{1+1+2SinA}{(CosA.1+SinA)}}}$ $\mathrm\blue{\rightarrow{\dfrac{2+2SinA}{(CosA.1+SinA)}}}$ $\mathrm\blue{\rightarrow{\dfrac{2(1+SinA)}{(CosA)(1+SinA)}}}$ $\mathrm\blue{\rightarrow{\dfrac{2{\red{\cancel{\blue{(1+SinA)}}}}}{(CosA){\red{\cancel{\blue{(1+SinA)}}}}}}}$ $\mathrm\blue{\rightarrow{\dfrac{2}{CosA}}}$ $\mathrm\blue{\rightarrow{2SecA}}$ $\sf{\boxed{\boxed{\pink{\rightarrow{2SecA{\color{black}{\checkmark}}}}}}}$ ☞ *HENCE* *2SecA* is *the* *REQUIRED* *answer. HOPE* IT *HELPS*.

Answer»

$\huge\rm{\underline{\underline{Given\rightarrow}}}$