Question

can you plz solve this for a 100 points​

Answer 1

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Solution

Answer 2

$\huge \underline{ \underline{ \bf{ solution}}} : -$

According to the question:-

$\frac{ \cot(a ) \cos(a) }{ \cot(a) + \cos(a) } = \frac{ \cot(a) - \cos(a) }{ \cot(a) \: \cos(a) } \\ \\ taking \: left \: hand \: side \\ \\ \implies \: \frac{ \cot(a ) \cos(a) }{ \cot(a) + \cos(a) } \\ \\ rationalising \: by \: \: \: \cot(a) - \cos(a) \\ \\ \implies \: \frac{ \cot(a) \cos(a) \big( \cot(a) - \cos(a) \big) }{ { \cot}^{2} a \: - { \cos }^{2}a } \\ \\ \implies \: \frac{ \: \cot(a) \cos(a) \big( \cot(a) - \cos(a) \big) \: }{ \frac{ { \cos }^{2} a}{ { \sin}^{2} a} \bigg(1 - { \sin }^{2} a \bigg)} \\ \\ \implies \: \frac{ \: \: \cot(a) \cos(a) \big( \cot(a) - \cos(a) \big) \: \: }{ \frac{ { \cos}^{4}a }{ { \sin}^{2} a} } \\ \\ \implies \: \frac{ \sin \: a}{ { \cos}^{2}a } \bigg( \cot \: a \: - \cos \: a \bigg) \\ \\ \implies \: \frac{ \cot \: a - \cos \: a }{ \cos \: a \: . \cot \: a}$

Hence proved .