Question

The value of $tan{58}^{\circ }tan{32}^{\circ }tan{57}^{\circ }tan{33}^{\circ }$ is

• A. 2
• B. 3
• C. 1
• D. 0

Answer 1

The correct option is C

1

$tan{32}^{\circ }=tan({90}^{\circ }-{58}^{\circ }$)
$=cot{58}^{\circ }$

$tan{33}^{\circ }=tan({90}^{\circ }-{57}^{\circ }$)
$=cot{57}^{\circ }$

Therefore,
$tan{58}^{\circ }tan{32}^{\circ }tan{57}^{\circ }tan{33}^{\circ }$
= $tan{58}^{\circ }cot{58}^{\circ }tan{57}^{\circ }cot{57}^{\circ }$
= $tan{58}^{\circ }\frac{1}{tan{58}^{\circ }}tan{57}^{\circ }\frac{1}{tan{57}^{\circ }}$
[since cot A=$\frac{1}{tanA}$]
=1