Question

given △def, which is not equal to cos(f)? sin(f). sin(d). tan(f). cos(d).

Explanation:

Step1: Recall trigonometric - ratio definitions

In right - triangle $\triangle DEF$ with right - angle at $E$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Also, note that $\cos D=\sin F$ and $\cos F = \sin D$ in a right - triangle (co - function identities: $\cos(90^{\circ}-\alpha)=\sin\alpha$).

Step2: Calculate each trigonometric ratio

For $\angle D$, $\sin D=\frac{EF}{DF}=\frac{5}{5\sqrt{2}}=\frac{1}{\sqrt{2}}$, $\cos D=\frac{DE}{DF}=\frac{5}{5\sqrt{2}}=\frac{1}{\sqrt{2}}$.
For $\angle F$, $\sin F=\frac{DE}{DF}=\frac{5}{5\sqrt{2}}=\frac{1}{\sqrt{2}}$, $\cos F=\frac{EF}{DF}=\frac{5}{5\sqrt{2}}=\frac{1}{\sqrt{2}}$, $\tan F=\frac{DE}{EF}=\frac{5}{5} = 1$.

Answer:

$\tan(F)$