Question
Without using trigonometric table, evaluate:
$
\cos e c 49^{\circ} \cos 41^{\circ}+\frac{\tan 31^{\circ}}{\cot 59^{\circ}}
$
$
\cos e c 49^{\circ} \cos 41^{\circ}+\frac{\tan 31^{\circ}}{\cot 59^{\circ}}
$
✓
Answer
$
\begin{aligned}
& \operatorname{cosec} 49^{\circ} \cos 41^{\circ}+\frac{\tan 31^{\circ}}{\cot 59^{\circ}} \\
& \Rightarrow \sec \left(90^{\circ}-41^{\circ}\right) \cos 41^{\circ}+\frac{\cot \left(90^{\circ}-59^{\circ}\right)}{\cot 56^{\circ}} \\
& \Rightarrow \sec 41^{\circ} \cos 41^{\circ}+\frac{\cot 59^{\circ}}{\cot 59^{\circ}}=1+1=2
\end{aligned}
$
\begin{aligned}
& \operatorname{cosec} 49^{\circ} \cos 41^{\circ}+\frac{\tan 31^{\circ}}{\cot 59^{\circ}} \\
& \Rightarrow \sec \left(90^{\circ}-41^{\circ}\right) \cos 41^{\circ}+\frac{\cot \left(90^{\circ}-59^{\circ}\right)}{\cot 56^{\circ}} \\
& \Rightarrow \sec 41^{\circ} \cos 41^{\circ}+\frac{\cot 59^{\circ}}{\cot 59^{\circ}}=1+1=2
\end{aligned}
$
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