Answer
$\tan 4^{\circ} 30'$ = $0.0787$
$\cot 85^{\circ} 30'$= $0.0787$
Thus, results justify the Cofunction Theorem.
Work Step by Step
Given pair is-
$\tan 4^{\circ} 30'$ , $\cot 85^{\circ} 30'$
As 60' = $1^{\circ}$, therefore 30' = $0.5^{\circ}$
Hence pair becomes-
$\tan 4.5^{\circ} $ , $\cot 85.5^{\circ}$
Using reciprocal identity for $\cot$-
$\tan 4.5^{\circ} $ , $\frac{1}{\tan85.5^{\circ}}$
Using calculator in degree mode-
(4.5 → $\tan$) and ( 85.5 → $\tan$)
$0.0787017068$ , $\frac{1}{12.706204736}$
Now using calculator for reciprocal as required-
$0.0787017068$ , $0.0787017068$
Rounding to four places past the decimal point-
$0.0787$ , $0.0787$
i.e
$\tan 4^{\circ} 30'$ = $0.0787$
$\cot 85^{\circ} 30'$= $0.0787$
Thus, results justify the Cofunction Theorem.
