Question

Cos A upon 1 + sin a + 1 + sin a upon Cos A equal to 2 sec A

Answer 1

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Answer 2

$\huge\star{\red{\underline{\mathfrak{Answer :-}}}}$

Question :-

$\dfrac{ \cos \: A }{1 + \sin \: A} + \frac{1 + \sin \: A}{ \cos \: A} = 2 \sec \: A$

Let's prove this...!!!

LHS :-

$\leadsto {\dfrac{ {( \cos \: A )}^{2} + {(1 + \sin \: A) }^{2} }{(1 + \sin \: A)( \cos \: A) }}$

$\leadsto {\dfrac{ { (\cos \: A) }^{2} + 1 + { (\sin \: A) }^{2} + 2 \sin \: A }{ \cos A + (\sin A )(\cos A) } }$

$\leadsto {\dfrac {1 - \cancel {{sin A}^{2}} + 1 +\cancel {{sin A}^{2}} + 2 \sin A}{\cos A + (\sin A)(\cos A)}}$

$\leadsto{\dfrac{2 + 2 \sin A}{\cos A + (\sin A)(\cos A)}}$

$\leadsto {\dfrac {2 \cancel{(1 + \sin A)}}{ \cos A \cancel{(1 + \sin A)}}}$

$\leadsto {\dfrac {2}{\cos A}}$

$\leadsto {2 \sec A}$

$\therefore {Hence\:proved}$