Question

if tan theta=4/3, find the value of 1-sin theta / 1 + sin theta

Answer 1

Answer:

1/9

Step-by-step explanation:

Tan∅ = Opposite / Adjacent Side

Tan∅ = 4/5

SUBSTITUTE THIS IN A TRIANGLE

By using Pythagoras theorem,

AC²=AB²+BC²

AC²=4²+3²

AC²=16+9

AC²=25

AC=5

NOW,

sin∅  =  Opposite Side / Hypotenuse

        = 4/5

Therefore,

1-sin∅ / 1+sin∅

= 1 - 4/3 / 1 + 4/3

= 1/9

Answer 2

$since \: \tan( \alpha ) = \frac{perpendicular}{base}$
$therefore \: \frac{perpendicular}{base} = \frac{4}{3}$
$thus \: perependicular = 4 \: and \: base = 3$
therefore by Pythagoras theorem
$(hypotenuse) {}^{2} = (perpendicular) {}^{2} + (base) {}^{2}$
let hypotenuse is h, perpendicular is p and base of a triangle is b

$therefore \: h {}^{2} = 4 {}^{2} + 3 {}^{2}$
$= 16 + 9 = 25$
$h = \sqrt{25} = 5$
$therefore \: \sin( \alpha ) = \frac{p}{h} = \frac{4}{5}$
$= \frac{1 - \sin( \alpha ) }{1 + \sin( \alpha ) } = \frac{1 - \frac{4}{5} }{1 + \frac{4}{5} }$
$= \frac{1}{9}$