Question

for an acute angle thita , prove that :
tan thita=sin thita /cos thita

Answer 1

We know,

$\tan( \alpha ) = \frac{height}{perpendicular}$



Then, divide both denominator and Nominator by hypotenuse,


$\tan( \alpha ) = \frac{ \frac{height}{hypotenuse} }{ \frac{base}{hypotenuse} }$

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We know,
$\sin( \alpha ) = \frac{heght}{hypotenuse} \\ \\ \cos( \alpha ) = \frac{base}{hypotenuse}$

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Then,


$\tan( \alpha ) = \frac{ \frac{height}{hypotenue} }{ \frac{base}{hypotenuse} } = \frac{ \sin( \alpha ) }{ \cos( \alpha ) }$



Hence, proved.


I hope this will help you


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