Evaluate : 3 cos 80° cosec 10° + 2 cos 59° cosec 31°

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Evaluate : 3 cos 80° cosec 10° + 2 cos 59° cosec 31°

1. 1
2. 3
3. 2
4. 5

Correct Option: D

3 cos 80°. cosec 10° + 2 cos 59° . cosec 31°
= 3cos(90°–10°). cosec 10° + 2 cos(90°– 31°) . cosec 31°
= 3 sin 10°. cosec 10° + 2 sin 31°. cosec 31°
= 3 + 2 = 5
[ ∵ cos (90°– θ) = sinθ ; sinθ . cosecθ = 1]