Question

simplify the expression
±√(1 - cos100)/(1 + cos100)
±√(1 - cos100)/(1 + cos100)=□
(simplify your answer. use integers or fractions for any numbers in the expression)

Explanation:

Step1: Use the half - angle identity

We know that \(\tan\frac{\alpha}{2}=\pm\sqrt{\frac{1 - \cos\alpha}{1+\cos\alpha}}\). Here \(\alpha = 100\), so \(\pm\sqrt{\frac{1-\cos100}{1 + \cos100}}=\tan\frac{100}{2}\).

Step2: Calculate the value

\(\tan\frac{100}{2}=\tan50\).

Answer:

\(\tan50\)