Question
Prove that:
$\frac{\cos80^\circ}{\sin10^\circ}+\cos59^\circ\text{cosec }31^\circ=2$
$\frac{\cos80^\circ}{\sin10^\circ}+\cos59^\circ\text{cosec }31^\circ=2$
✓
Answer
$\cos80^\circ=\cos(90^\circ-10^\circ)=\sin10^\circ$
$\cos59^\circ=\cos(90^\circ-31^\circ)=\sin31^\circ$
$\Rightarrow\frac{\sin10^\circ}{\sin10^\circ}+\sin31^\circ\text{cosec }31^\circ$
$=1+1=2$ $[\because\sin\theta\text{ cosec }\theta=1]$
Hence proved.
$\cos59^\circ=\cos(90^\circ-31^\circ)=\sin31^\circ$
$\Rightarrow\frac{\sin10^\circ}{\sin10^\circ}+\sin31^\circ\text{cosec }31^\circ$
$=1+1=2$ $[\because\sin\theta\text{ cosec }\theta=1]$
Hence proved.
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