Question

sin²(5°) + sin²(10°) + sin²(15°) + ... + sin²(85°) + sin²(90°) = ______.

विकल्प

• `9/2`

• `19/2`

• `39/2`

• `49/2`

Answer 1

sin²(5°) + sin²(10°) + sin²(15°) + ... + sin²(85°) + sin²(90°) = `19/2`.

Explanation:

sin²(5°) + sin²(10°) + sin²(15°) + ... + sin²(85°) + sin²(90°)

= sin²(5°) + sin²(10°) + ... + cos²(10°) + cos²(5°) + sin²(90°)  .....[∵ sin(90° – θ) = cos θ]

= [sin²(5°) + cos²(5°)] + ... + [sin²(40°) + cos²(40°)] + sin²(30°) + sin²(45°) + sin²(60°) + sin²(90°)

= `(1 + 1 + ... + 1) + (1/2)^2 + (1/sqrt(2))^2 + (sqrt(3)/2)^2 + (1)^2`

= `7 + 1/4 + 1/2 + 3/4 + 1`

= `19/2`