Question

(cos A/1+sin A )+(1+sin A/cosA)​

Answer 1

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 2

Given :

$\sf {\dfrac{(CosA)}{(1+SinA)}+\dfrac{(1+SinA)}{(CosA)}}$

Need to Do :

• Simplification ?

Solution :

$: \implies \sf{\dfrac{(CosA)}{(1+SinA)}+\dfrac{(1+SinA)}{(CosA)}}$

$: \implies \sf{\dfrac{(CosA.CosA)}{(1+SinA.CosA)}+\dfrac{(1+SinA.1+SinA)}{(CosA.1+SinA)}}$

$: \implies \sf{ \dfrac{(Cos^2A)}{(1+SinA.CosA)}+\dfrac{(1+SinA)^2}{(CosA.1+SinA)}</p><p> }$

$: \implies \sf{\dfrac{Cos^2A+(1+SinA)^2}{(CosA.1+SinA)}}$

$: \implies \sf{\dfrac{Cos^2A+1+Sin^2A+2SinA)}{(CosA.1+SinA)}}$

$: \implies \sf {\dfrac{Cos^2A+Sin^2A+2SinA+1}{(CosA.1+SinA)}}$

$: \implies \sf{\dfrac{1+1+2SinA}{(CosA.1+SinA)}}$

$: \implies \sf {\dfrac{2+2SinA}{(CosA.1+SinA)}}$

$: \implies \sf{\dfrac{2(1+SinA)}{(CosA)(1+SinA)}}$

$: \implies \sf{\dfrac{2{\cancel{(1+SinA)}}}{(CosA){\cancel{(1+SinA)}}}}$

$: \implies \sf{\dfrac{2}{CosA}}$

$:\implies{\boxed{\sf{\pink{2\;secA}}}}\;\bigstar$

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