Question

Given that I

cos(A-B)
cos(A+B)
5
4.
find the value of
cot(A) cot(B)
a) -1
b) -5/4
c) 1/4
d) 5/4

Answer 1

To find the value of cot(A) cot(B) when cos(A-B) cos(A+B) = 5/4, use the cosine addition formula and rearrange the equation.

Step-by-step explanation:

To find the value of cot(A) cot(B) when cos(A-B) cos(A+B) = 5/4, we can use the cosine addition formula cos(A-B) cos(A+B) = cos(A) cos(B) + sin(A) sin(B). Since we are given that cos(A-B) cos(A+B) = 5/4, we have cos(A) cos(B) + sin(A) sin(B) = 5/4.

Next, we can use the fact that cot(A) = cos(A) / sin(A) and cot(B) = cos(B) / sin(B). Rearranging the equation, we have cos(A) cos(B) = (5/4) - sin(A) sin(B).

Finally, substituting in the expressions for cot(A) and cot(B), we get cot(A) cot(B) = (cos(A) / sin(A)) (cos(B) / sin(B)) = (5/4) - sin(A) sin(B).