The value of tan80° tan10° + sin2 70° + sin270° + sin220°

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The value of tan80° tan10° + sin2 70° + sin²70° + sin²20° is

1. 0
2. 1
3. 2
4. √3
  2

Correct Option: C

tan 80° . tan 10° + sin²70° + sin²20°
= tan (90° – 10°) . tan 10° + sin²(90° – 20°) + sin²20°
= cot 10° . tan 10° + cos²20° + sin²20°
= 1 + 1 = 2
[∵ sin (90° – θ) = cosθ; tan (90° – θ) = cotθ; tanθ . cotθ = 1]