Question

if 4 sin theta is equal to 5 find the value of tan theta cos theta

Answer 1

$4 \sin( \alpha ) = 5(given)$
$= \sin( \alpha ) = \frac{5}{4}$
$but \: \sin( \alpha ) = \frac{perpendicular }{hypotenouse}$
$= \frac{5}{4} = \frac{perpendicular}{hypotenouse}$
$= {base}^{2} = {hypotenouse}^{2} - {perpendicular}^{2} (pythagoras theorem)$
${base}^{2} = ({5x})^{2} - ({4x})^{2}$

${base}^{2} = 25 {x }^{2} - 16 {x}^{2}$
${base}^{2} = 9 {x}^{2}$
$base = 3x$
$\tan( \alpha ) = \frac{perpendicular}{base}$
$= \tan( \alpha ) = \frac{4x}{3x}$
$= \tan( \alpha ) = \frac{4}{3}$
$also \\ \cos( \alpha ) = \frac{base}{hypotenouse}$
$= \cos( \alpha ) = \frac{3x}{5x}$
$\cos( \alpha ) = \frac{3}{5}$

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Answer 2

1-sin theta=cos theta