Question

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

Explanation:

Step1: Recall trig - ratio definitions

In right - triangle $\triangle DEF$ with right - angle at $E$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Also, $\cos(F)=\sin(D)$ (co - function identity).

Step2: Analyze each option

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

Answer:

B. $\tan(F)$