Question

Determine the value of \tan20\degree +\tan40\degree+ \sqrt{3}\tan 20\degree\cdotp\tan40\degree

Collected in the board: Trigonometry

Steven Zheng posted 1 month ago


Answer

\tan 60\degree =\tan(20\degree +40\degree )

=\dfrac{\tan20\degree +\tan40\degree}{1-\tan 20\degree\cdotp\tan40\degree} =\sqrt{3}

Therefore,

\tan20\degree +\tan40\degree = \sqrt{3}-\sqrt{3}\tan 20\degree\cdotp\tan40\degree

\tan20\degree +\tan40\degree+ \sqrt{3}\tan 20\degree\cdotp\tan40\degree =\sqrt{3}

Steven Zheng posted 1 month ago

Scroll to Top