Question

for what value of acute angle . cosA/ 1-sinA + cosA/ 1+ sinA​

Answer 1

Given :

$\implies\bf\dfrac{ \cos A}{1 - \sin A} + \dfrac{ \cos A}{1 + \sin A}$

By taking LCM

$\implies\bf\frac{ \cos A+ \sin A\cos A + \cos A - \sin A \cos A }{(1 - \sin A)(1 + \sin A)} \\ \\ \implies\bf \frac{\cos A+ \cos A}{1 - { \sin}^{2} A} \\ \\ \implies\bf \frac{ \cos A+ \cos A}{ { \cos}^{2} A } \\ \\ \implies\bf \frac{ \cos A}{ \ { \cos}^{2}A } + \frac{ \cos A}{ \ { \cos}^{2}A } \\ \\\implies\bf \frac{1}{ \cos A} + \frac{1}{ \cos A} \\ \\\implies\bf \sec A+ \sec A\\ \\ \implies\bf \large2 \sec A$

Answer 2

Step-by-step explanation:

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