Step 1: To subtract a fraction from a whole number, the whole number needs to be expressed as a fraction with the same denominator as the fraction being subtracted. In the expression $1 - \frac{9}{25}$, the denominator of the fraction is $25$. Step 2: To express $1$ as a fraction with a denominator of $25$, we multiply $1$ by $\frac{25}{25}$ (which is equivalent to $1$). $$ 1 = 1 \times \frac{25}{25} = \frac{25}{25} $$ Step 3: Now, substitute $\frac{25}{25}$ back into the equation: $$ \cos^2 \theta = \frac{25}{25} - \frac{9}{25} $$ This allows for direct subtraction of the numerators.