If 15Cot=8, find (1+SinA)(1-SinA)/(1+CosA)(1-CosA)
cotA = 8/15
tanA = 15/8
so y=15, x=8
r^2 = 15^2 + 8^2
r = √289 = 17
sinA = 15/17
cosA = 8/17
then (1+SinA)(1-SinA)/(1+CosA)(1-CosA)
= (1 - sin^2 A)/(1 - cos^2 A)
= (1 - 225/289)/(1 - 64/289)
= (64/289) / (225/289)
= 64/225
To find the value of (1+sinA)(1-sinA)/(1+cosA)(1-cosA), we need to utilize the given equation 15cotA = 8. Let's start by finding the values of sinA and cosA using the given information.
We know that cotA = 1/tanA, so we can rewrite the equation 15cotA = 8 as 15/tanA = 8.
To find tanA, we can rearrange the equation as tanA = 15/8. We can then use the definition of tangent, which is sinA/cosA, to find the values of sinA and cosA.
So, we have sinA/cosA = 15/8.
To eliminate the fraction, we can multiply both sides of the equation by 8cosA, resulting in sinA = (15/8)cosA.
Now, we can substitute this value back into the equation (1+sinA)(1-sinA)/(1+cosA)(1-cosA), since we have found sinA in terms of cosA.
(1 + (15/8)cosA)(1 - (15/8)cosA) / (1 + cosA)(1 - cosA)
Simplifying this expression further may require additional information or restrictions on the values of A. If you have any additional information or restrictions, please provide them, and I can assist you further.