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