Question
Evaluate $: 3 \cos 80^\circ \operatorname{cosec} 10^\circ + 2 \sin 59^\circ \sec 31^\circ .$
✓
Answer
$ 3 \cos 80^\circ \operatorname{cosec} 10^\circ + 2 \sin 59^\circ \sec 31^\circ$
$= 3 \cos (90^\circ - 10^\circ ) \operatorname{cosec} 10^\circ + 2\sin (90^\circ - 31) \sec 31^\circ$
$= 3 \sin 10^\circ \operatorname{cosec} 10^\circ + 2 \cos 31^\circ \sec 31^\circ$
$= 3 \times 1 + 2\times1$
$= 3 + 2$
$= 5$
$= 3 \cos (90^\circ - 10^\circ ) \operatorname{cosec} 10^\circ + 2\sin (90^\circ - 31) \sec 31^\circ$
$= 3 \sin 10^\circ \operatorname{cosec} 10^\circ + 2 \cos 31^\circ \sec 31^\circ$
$= 3 \times 1 + 2\times1$
$= 3 + 2$
$= 5$
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