Question

(1+sin tita) (1-sin tita) / (1+cos tita) (1-cos tita​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

cot^2 theta

(1 + sin theta)(1 - sin theta) / (1 + cos theta)(1 - cos theta) = cot^2 theta

Step-by-step explanation:

Given,

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

We know that,

(a + b)(a - b) = a^2 - b^2

On applying this identity, we get,

= (1 - sin^2 theta) / (1 - cos^2 theta)

Also,

sin^2 theta + cos^2 theta = 1

Then, we can derive,

sin^2 theta = 1 - cos^2 theta

cos^2 theta = 1 - sin^2 theta

On applying this in the equation, we get,

= cos^2 theta / sin^2 theta

We know that,

cot theta = cos theta / sin theta

Then,

cos^2 theta / sin^2 theta = cot^2 theta

Hence,

(1 + sin theta)(1 - sin theta) / (1 + cos theta)(1 - cos theta) = cot^2 theta