Question

show that cot π+tanπ=secπ.cosecπ
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Answer 1

Step-by-step explanation:

$given \: equation \: \\ cot\pi + tan\pi$

$we \: know \: that \: cot\pi = \frac{1}{tan\pi}$

$substitute \: in \: the \: equation \:$

$\frac{1}{ \tan(\pi) } + \tan(\pi)$

$take \: lcm$

$\frac{1 + { (\tan(\pi)) }^{2} }{ \tan(\pi) }$

$we \: know \: that \: \: 1 + {( \tan(\pi)) }^{2} = { (\sec(\pi) )}^{2}$

$hence \: the \: equation \: can \: be \: written \: as \:$

$\frac{ { (\sec(\pi) )}^{2} }{ \tan(\pi) }$

${ (\sec(\pi)) }^{2} \times \frac{ \cos(\pi) }{ \sin(\pi) }$

$\sec(\pi) \times \cos(\pi) \times \sec(\pi) \times \csc(\pi) \\ = 1 \times \sec(\pi) \times \csc(\pi ) \\ = \sec(\pi) \times \csc(\pi)$

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