Evaluate : 3cos80°.cosec10° + 2cos59°.cosec31°

Answer: Option D

3cos80°.cosec10° + 2cos59°.cosec31°
[If A + B = 90° then, cosA.cosecB = 1]
(3 × 1 + 2 × 1 = 5)
(the value of sinθ is always between -1 to +1)
  $$\Rightarrow \text{3cos8}{\text{0}}^{\circ }\frac{1}{\sin {10}^{\circ }}\text{ + 2cos5}{\text{9}}^{\circ }\frac{1}{\text{sin 3}{\text{1}}^{\circ }}$$
  $$\Rightarrow \text{3cos8}{\text{0}}^{\circ }\frac{1}{\sin \left({90}^{\circ }-{80}^{\circ }\right)}\text{ + }$$     $$\text{2cos5}{\text{9}}^{\circ }$$  $$\frac{1}{\text{sin }{\left({90}^{\circ }-{59}^{\circ }\right)}^{\circ }}$$
$$\begin{array}{rl}& \Rightarrow 3+2\\ & \Rightarrow 5\end{array}$$