Het product

tan 300°. cot 400°. tan 500°

is gelijk aan
 A.  \(\boldsymbol{\frac {\sqrt 3} {3} }\)
B.  \(\boldsymbol{\sqrt 3 }\)
C.  \(\boldsymbol{3}\)
D.  \(\boldsymbol{-\,\sqrt 3 }\)
E.  \(\boldsymbol{-\,\frac {\sqrt 3} {3}}\)
A    B    C    D    E 

[ 4-2065 - op net sinds 8.11.12-(E)-30.10.2023 ]

Translation in   E N G L I S H

The product

tan 300° × cot 400° × tan 500°

is equal to
A.   \(\boldsymbol{\frac {\sqrt 3} {3} }\)
B.   \(\boldsymbol{\sqrt 3 }\)
C.   \(\boldsymbol{3}\)
D.   \(\boldsymbol{-\,\sqrt 3 }\)
E.   \(\boldsymbol{-\,\frac {\sqrt 3} {3}}\)

Oplossing - Solution

  tan 300°.cot 400°.tan 500°
= tan (300° − 360°).cot (400° − 360°).tan (500° − 360°)
= tan(− 60°).cot 40°.tan 140°
= − tan 60°. cot 40°.(− tan 40°)
= tan 60° = . . .
gricha