Solution
Expression : 3 cos 80° cosec 10° + 2 cos 59° cosec 31°
= $$3 \frac{cos 80^{\circ}}{sin 10^{\circ}} + 2 \frac{cos 59^{\circ}}{sin 31^{\circ}}$$
= $$3 \frac{cos 80^{\circ}}{sin (90^{\circ} - 80^{\circ})} + 2 \frac{cos 59^{\circ}}{sin (90^{\circ} - 59^{\circ})}$$
= $$3 \frac{cos 80^{\circ}}{cos 80^{\circ}} + 2 \frac{cos 59^{\circ}}{cos 59^{\circ}}$$
= 3 + 2 = 5
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