Determine the exact values of the following:
b) (cos45)(tan45)
To begin, let's use the identity $\tan(\theta) = \frac{{\sin(\theta)}}{{\cos(\theta)}}$.
Given: $\cos(45°)\cdot\tan(45°)$
Using the identity, we have: $\cos(45°)\cdot\tan(45°) = \cos(45°)\cdot\frac{{\sin(45°)}}{{\cos(45°)}}$
Now, we can cancel out the $\cos(45°)$ term in the numerator and denominator, giving us: $\cos(45°)\cdot\frac{{\sin(45°)}}{{\cos(45°)}} = \sin(45°)$
The sine of $45°$ is equal to $\frac{1}{{\sqrt{2}}}$.
Therefore, $\cos(45°)\cdot\tan(45°) = \frac{1}{{\sqrt{2}}}$ or $\frac{{\sqrt{2}}}{{2}}$ (exact value).