Question

if cot theta=7/8, evaluate
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$\frac{(1 + sin(theta))(1 - sin(theta))}{(1 + \cos (theta))(1 - \cos (theta))}$
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. PLEASE DON'T SPAM OR YOUR ANSWER WILL BE REPORTED

Answer 1

Given that :

$\cot\alpha = \frac{7}{8} = \frac{b}{p}$

According to the Pythagoras theoram :

H² = P² + B²

=> H = √64+49 = √113

Now,

$\sin \alpha = \frac{p}{h} = \frac{8}{ \sqrt{113} }$

And,

$\cos \alpha = \frac{b}{h} = \frac{7}{ \sqrt{113} }$

According to the question :

$\frac{(1 + \sin\alpha)(1 - \sin \alpha ) }{(1 + \cos \alpha )(1 - \cos\alpha ) } \\ \\ = > \frac{1 - { \sin }^{2} \alpha }{1 - { \cos}^{2} \alpha } = \frac{1 - \frac{64}{113} }{1 - \frac{49}{113} } \\ \\ = > \frac{113 - 64}{113 - 49} = \frac{49}{64}$

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