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Answer 1

hey mate here is the answer✨✨✨✨✨

______________

I)

(1+sin theta)(1-sin theta)/(1+cos theta)(1-cos theta)

(1-sin²theta)/1-cos²theta)

1/1. ___________
[ 1-sin²theta=1 and 1-cos²theta=1]

1

ii)cot²theta

(7/8)²

49/64

______________

hope it's helpful

Answer 2

Heya mate,Here is ur answer

1)

Let us take theta as A

Given Cot A =7/8

1)
$\frac{(1 + sin \: a)(1 - sin \: a)}{(1 + cos \: a)(1 - cos \: a)}$


We know that (a+b)(a-b)=a^2 -b^2

$= \frac{1 {}^{2} - {sin \: }^{2}a }{1 {}^{2} - cos \: {}^{2}a }$


We know that 1 - sin ^2 A = cos ^A

And 1 - cos^2 A = Sin ^2 A


$= \frac{cos \: {}^{2}a }{sin \: {}^{2} a}$


We know that Cos A/ Sin A = Cot A

So,

$= cot { {}^{} }^{2} a$


$= ( \frac{7}{8}) {}^{2}$


$= \frac{49}{64}$


Also, Cot ^2 A =49/64

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Warm regards

@Laughterqueen

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