We are asked to fill in the blank to complete the following trigonometric formula.
cos ^2 u =
Note that the left-hand side of the formula contains a trigonometric function raised to the second power. This means that the given formula is one of the power-reducing formulas. Let's recall all of the power-reducing formulas.
Power-Reducing Formulas
sin ^2 u = 1-cos 2u/2
cos ^2 u = 1+cos 2u/2
tan ^2 u = 1-cos 2u/1+cos 2u
Next, let's look for the formula that contains the expression cos ^2 u.
Power-Reducing Formulas
sin ^2 u = 1-cos 2u/2
cos ^2 u = 1+cos 2u/2
tan ^2 u = 1-cos 2u/1+cos 2u
According to one of the formulas from the table, cos ^2 u is equal to 1+cos 2u2. With this in mind, let's complete the given formula.
cos ^2 u = 1+cos 2u/2
