{1+an²A\1+cot²A}= {1- tanA\cotA}²= tan ²A prove …
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Sia ? 6 years, 6 months ago
{tex}= \frac { 1 + \tan ^ { 2 } A } { 1 + \cot ^ { 2 } A } = \frac { 1 + \tan ^ { 2 } A } { 1 + \frac { 1 } { \tan ^ { 2 } A } } \cdot \because \cot A = \frac { 1 } { \tan A }{/tex}
{tex}= \frac { 1 + \tan ^ { 2 } A } { \frac { \tan ^ { 2 } A + 1 } { \tan ^ { 2 } A } } = \tan ^ { 2 } A \ldots \ldots ( 1 ){/tex}
{tex}\left( \frac { 1 - \tan A } { 1 - \cot A } \right) ^ { 2 } = \left( \frac { 1 - \tan A } { 1 - \frac { 1 } { \tan A } } \right) ^ { 2 }{/tex}
{tex}= \left\{ \frac { 1 - \tan A } { \left( \frac { \tan A - 1 } { \tan A } \right) } \right\} ^ { 2 } = ( - \tan A ) ^ { 2 } = \tan ^ { 2 } A{/tex} ....... (2)
(1) and (2) taken together given the result.
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