Question

Determine the value of \dfrac{1-\tan^2 75\degree }{1+\tan^2 75\degree }

Collected in the board: Trigonometry

Steven Zheng posted 2 months ago


Answer

\dfrac{1-\tan^2 75\degree }{1+\tan^2 75\degree }

=\dfrac{\dfrac{1}{1+\tan^2 75\degree} }{\dfrac{1}{1-\tan^2 75\degree} }


=\dfrac{\dfrac{2\tan 75\degree}{1+\tan^2 75\degree} }{\dfrac{2\tan 75\degree}{1-\tan^2 75\degree} }


=\dfrac{\sin 150\degree }{\tan 150\degree } =\cos 150\degree =-\dfrac{\sqrt{3} }{2}

Steven Zheng posted 2 months ago

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