Answer
$\tan 10^{\circ} 30'$ = $0.1853$
$\cot 79^{\circ} 30'$= $0.1853$
Thus, results justify the Cofunction Theorem.
Work Step by Step
Given pair is-
$\tan 10^{\circ} 30'$ , $\cot 79^{\circ} 30'$
As 60' = $1^{\circ}$, therefore 30' = $0.5^{\circ}$
Hence pair becomes-
$\tan 10.5^{\circ} $ , $\cot 79.5^{\circ}$
Using reciprocal identity for $\cot$-
$\tan 10.5^{\circ} $ , $\frac{1}{\tan79.5^{\circ}}$
Using calculator in degree mode-
(10.5 → $\tan$) and ( 79.5 → $\tan$)
$0.1853390449$ , $\frac{1}{5.3955171743}$
Now using calculator for reciprocal as required-
$0.1853390449$ , $0.1853390449$
Rounding to four places past the decimal point-
$0.1853$ , $0.1853$
i.e
$\tan 10^{\circ} 30'$ = $0.1853$
$\cot 79^{\circ} 30'$= $0.1853$
Thus, results justify the Cofunction Theorem.
