using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the expression as:
28/sin^2(31) + sin^2(59= 28/cos^2(59) + sin^2(59= 28/(1 - sin^2(59)) + sin^2(59)
Now, we can substitute sin^2(59) with x:
28/(1-x) + x
Now, we need to find the value of x:
sin^2(59) = sin^2(90-31) = sin^2(90)cos^2(31) = 1 * cos^2(31) = cos^2(31)
Therefore, x = cos^2(31)
Now, we can substitute x back into the expression:
28/(1 - cos^2(31)) + cos^2(31)
Using the identity sin^2(x) + cos^2(x) = 1, we know that:
1 - cos^2(x) = sin^2(x)
So the expression becomes:
28/sin^2(31) + sin^2(31)
= 28*sin^2(31) + sin^2(31)
= 29*sin^2(31)
Therefore, the final answer is 29*sin^2(31).
using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the expression as:
28/sin^2(31) + sin^2(59
= 28/cos^2(59) + sin^2(59
= 28/(1 - sin^2(59)) + sin^2(59)
Now, we can substitute sin^2(59) with x:
28/(1-x) + x
Now, we need to find the value of x:
sin^2(59) = sin^2(90-31) = sin^2(90)cos^2(31) = 1 * cos^2(31) = cos^2(31)
Therefore, x = cos^2(31)
Now, we can substitute x back into the expression:
28/(1 - cos^2(31)) + cos^2(31)
Using the identity sin^2(x) + cos^2(x) = 1, we know that:
1 - cos^2(x) = sin^2(x)
So the expression becomes:
28/sin^2(31) + sin^2(31)
= 28*sin^2(31) + sin^2(31)
= 29*sin^2(31)
Therefore, the final answer is 29*sin^2(31).