Can you write cos(\(\displaystyle \theta\)/2) and tan(\(\displaystyle \theta\)/2) in terms of sines and cosines? It is just the definition of cos(\(\displaystyle \theta\)/2) and tan(\(\displaystyle \theta\)/2)
Now can you label the three sides of a right triangle such that sec(\(\displaystyle \theta\)) = \(\displaystyle \sqrt{5}\)?
Now using this triangle and the half angle formulas can you now answer the questions?
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