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

Question

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

Uniteasy Admin · Accepted Answer

$$\dfrac{1-	an^2 75\degree }{1+	an^2 75\degree } $$
$$=\dfrac{\dfrac{1}{1+	an^2 75\degree} }{\dfrac{1}{1-	an^2 75\degree} } $$
$$=\dfrac{\dfrac{2	an 75\degree}{1+	an^2 75\degree} }{\dfrac{2	an 75\degree}{1-	an^2 75\degree} } $$
$$=\dfrac{\sin 150\degree }{	an 150\degree } =\cos 150\degree =-\dfrac{\sqrt{3} }{2}  $$

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