Question

use the given triangle to evaluate the expression. if necessary, express the value without a square root in the denominator by rationalizing the denominator. cos(π/4) - sin(π/4) cos(π/4) - sin(π/4) = (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions)

Explanation:

Step1: Recall trigonometric values

For an angle of $\frac{\pi}{4}$ (or 45 - degrees), $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$ and $\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$.

Step2: Substitute values

Substitute $\cos\frac{\pi}{4}$ and $\sin\frac{\pi}{4}$ into the expression $\cos\frac{\pi}{4}-\sin\frac{\pi}{4}$. We get $\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}$.

Step3: Calculate the result

$\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}=0$.

Answer:

$0$