Answer: bellow .
Explanation:
To find the value of sin^2(2 deg) + sin^2(3 deg) + sin^2(88 deg) + sin^2(87 deg), we can use the trigonometric identity:
sin^2(x) + cos^2(x) = 1
Since the question is asking for the sum of four terms, we can use this identity to simplify the expression:
sin^2(2 deg) + sin^2(3 deg) + sin^2(88 deg) + sin^2(87 deg) = 1 - cos^2(2 deg) + 1 - cos^2(3 deg) + 1 - cos^2(88 deg) + 1 - cos^2(87 deg)
Next, let's use the fact that cos(x) = sin(90 deg - x):
= 1 - cos^2(2 deg) + 1 - cos^2(3 deg) + 1 - cos^2(2 deg) + 1 - cos^2(3 deg)
Now, we can use the identity sin^2(x) = 1 - cos^2(x):
= 1 - cos^2(2 deg) + 1 - cos^2(3 deg) + 1 - cos^2(2 deg) + 1 - cos^2(3 deg)
= 4 - (cos^2(2 deg) + cos^2(3 deg) + cos^2(2 deg) + cos^2(3 deg))
= 4 - 2(cos^2(2 deg) + cos^2(3 deg))
Now, we can substitute the values of cos(2 deg) and cos(3 deg) using a calculator or trigonometric tables. After calculating the values, we can plug them back into the expression:
= 4 - 2(0.99939^2 + 0.99863^2)
= 4 - 2(0.99878 + 0.99727)
= 4 - 2(1.99505)
= 4 - 3.9901
= 0.0099
Therefore, sin^2(2 deg) + sin^2(3 deg) + sin^2(88 deg) + sin^2(87 deg) is approximately equal to 0.0099.