a)
A = sin²15° + sin²40° + sin²60° + sin²75° + sin²50° + sin²30°
A = (sin²15° + cos²75°) + (sin²40° + cos²40°) + (sin²60° + cos²60°)
A = 1 + 1 + 1
A = 3
b)
B = tan5°tan10°...tan85°
B = tan5°cot5°tan10°cot10°tan15°cot15°tan20°cot20°tan25°cot25°tan30°cot30°tan35°cot35°tan40°cot40°...cot85°
B = 1
c)
cos²15° - cos²25° + cos²35° - cos²45° + cos²55° - cos²65° + cos²75°
= (cos²15° + sin²15°) - (cos²25° - sin²25°) + (cos²35° + sin²35°) - sqrt(2)^2
= (cos²15° + sin²15°) + (cos²25° + sin²25°) + (cos²35° + sin²35°) - sqrt(2)^2
= 1 + 1 + 1 - sqrt(2)^2 = 3 + 1/2 = 7/2