(CosecA -cot A)2=1-cos A÷1+cosA
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Sia ? 6 years, 4 months ago
LHS=(cosecA - cotA)2 = {tex}\left( \frac { 1 } { \sin A } - \frac { \cos A } { \sin A } \right) ^ { 2 }{/tex}
{tex}= \left( \frac { 1 - \cos A } { \sin A } \right) ^ { 2 }{/tex}
{tex}= \frac { ( 1 - \cos A ) ^ { 2 } } { \sin ^ { 2 } A }{/tex}
{tex}= \frac { ( 1 - \cos A ) ^ { 2 } } { 1 - \cos ^ { 2 } A }{/tex}
{tex}= \frac { ( 1 - \cos A ) ^ { 2 } } { ( 1 - \cos A ) ( 1 + \cos A ) }{/tex}
{tex}= \frac { 1 - \cos A } { 1 + \cos A }{/tex}
Hence proved
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