What is the value of the expression: sin²(1°) + sin²(11°) + sin²(21°) + sin²(31°) + sin²(41°) + sin²(45°) + sin²(49°) + sin²(59°) + sin²(69°) + sin²(79°) + sin²(89°)?

Correct option is D

Given:

We are asked to compute the sum of squares of sine values at various angles.

Formula/Property Used:

We use the identity: sin²(θ) + sin²(90° − θ) = 1

Solution:

Pairs that sum up:
· sin²(1°) + sin²(89°) = 1
· sin²(11°) + sin²(79°) = 1
· sin²(21°) + sin²(69°) = 1
· sin²(31°) + sin²(59°) = 1
· sin²(41°) + sin²(49°) = 1
Middle angle: sin²(45°) = 1/2

Sum = 5 pairs of 1 + 1/2 = 5 × 1 + 1/2 = 5.5
Hence,
Final Answer: (d) 5½