80^ 10^ + 59^ 31^ = _______. - Vidyadip

Question

$\frac{\cos80^\circ}{\sin10^\circ}+\cos59^\circ\text{cosec}31^\circ=$ _______.

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Answer

$\frac{\cos80^\circ}{\sin10^\circ}+\cos59^\circ\text{cosec}31^\circ=$ 2.Solution:
$\frac{\cos80^\circ}{\sin10^\circ}+\cos59^\circ\text{cosec}31^\circ$ $=\frac{\cos(90^\circ-10^\circ)}{\sin10^\circ}+\cos59^\circ\text{cosec}(90^\circ-59^\circ)$ $=\frac{\sin10^\circ}{\sin10^\circ}+\cos59^\circ\sec59^\circ$ $=1+1 = 2$

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