Question

The question asked by Agnel025❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️


Answer fast guys ​

Answer 1

Answer:

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Answer 2

$\underline{ \ \fbox{ \mathtt{ \huge{ \purple{ \: To \: prove : \: \: \: }}}}}$

$\red \star \: \: \sf { \frac{ \sec( \theta) }{ \sin( \theta) } - \frac{ \sin( \theta) }{ \cos( \theta) } } = \sf \cot( \theta)$

$\underline{ \ \fbox{ \mathtt{ \huge{ \purple{ \: Proof : \: \: \: }}}}}$

LHS

$\sf \hookrightarrow \frac{ \sec( \theta) }{ \sin( \theta) } - \frac{ \sin( \theta) }{ \cos( \theta) } \\ \\ \sf \hookrightarrow \frac{1}{ \sin( \theta) \times \cos( \theta) } - \frac{ \sin( \theta) }{ \cos(\theta) } \: \: \: \bigg \{ \because \sec( \theta) = \frac{1}{\cos( \theta) } \bigg\} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: Taking \: LCM \: , \: we \: get </p><p> \\ \\ \sf \hookrightarrow \frac{ 1 - { \sin}^{2}( \theta) }{\sin( \theta) \times \cos( \theta) } \\ \\ \sf \hookrightarrow \frac{ { \cos}^{ {2}}( \theta) }{\sin( \theta) \times {\cos( \theta)} } \: \: \: \bigg \{ \because 1 - { \sin}^{2} ( \theta) = { \cos}^{2} ( \theta) \bigg\} \\ \\ \sf \hookrightarrow \frac{ \cos( \theta)}{ \sin( \theta)} \\ \\ \sf \hookrightarrow \cot( \theta) \: \: \: \bigg \{\because \frac{ \cos( \theta)}{ \sin( \theta)} =\cot( \theta) \bigg\}$

LHS = RHS

Hence proved