2002 #10 and 32

Fractions and reasoning!

Difficulty: Pretty easy, for us old fogies who aren't scared of fractions.

Difficulty: Double angle formula. Yum. Algebra. Yummier.

Standard instructions for this series: No calculator allowed. Express  answers in reduced form. Rationalize denominators. Radicals must be  reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for  example. Source: UVM Math Contest

answer 10 and answer 32.