Question

Prove the equality given in the attachment. ​

Answer 1

Answer:

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LHS.

$\frac{1}{ \cos \: A + \sin A - 1} + \frac{1}{ \cos \:A + \sin \: A +1 }$

$= \frac{ \cos \: A + \sin \:A + 1 \cos \: A + \sin \: A }{( \cos \: A + \sin \: A) {}^{2} - 1}$

2(cosA+sinA)/sos^2+sin^2 A +2cos A sinA-1

$= \frac{2( \cos \:A + \sin \:A) }{1 + 2 \cos \: A \sin \: A } = \frac{ \cos \: A + \sin \: A }{ \cos \:A \sin \: A}$

$= \frac{ \cos \: A}{ \cos \: A \sin \: A} + \frac{ \sin \: A }{ \cos \: A \: \sin \: A }$

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

=cosecA + secA= RHS.

$\huge\mathbb{\underline{vertified \: answer}}$

Answer 2

Answer:

This is your answer

Step-by-step explanation:

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