Question

Say yes or no.
$\tan {48}^{\circ }\tan {23}^{\circ }\tan {42}^{\circ }\tan {67}^{\circ }=1$

• A. Yes
• B. No
• C. Ambiguous
• D. Data insufficient
  

Answer 1

The correct option is A Yes

$LHS=\tan {48}^{\circ }\tan {23}^{\circ }\tan {42}^{\circ }\tan {67}^{\circ }$
$=\tan {48}^{\circ }\times \tan {23}^{\circ }\times \tan ({90}^{\circ }-{48}^{\circ })\times \tan ({90}^{\circ }-{23}^{\circ })$
$=\tan {48}^{\circ }\times \tan {23}^{\circ }\times cot{48}^{\circ }\times cot{23}^{\circ }$
$=\tan {48}^{\circ }\times \tan {23}^{\circ }\times \frac{1}{\tan {48}^{\circ }}\times \frac{1}{\tan {23}^{\circ }}=1$
$\therefore LHS=RHS$