given △def, which is not equal to cos(f)?\no sin(f).\no sin(d).\no tan(f).\no cos(d).

Explanation:

Step1: Recall trigonometric relations in a right - triangle

In a right - triangle $\triangle DEF$ with right - angle at $E$, $\cos(F)=\frac{EF}{DF}$, $\sin(F)=\frac{DE}{DF}$, $\sin(D)=\frac{EF}{DF}$, $\tan(F)=\frac{DE}{EF}$, $\cos(D)=\frac{DE}{DF}$.

Step2: Compare each option with $\cos(F)$

We know that $\cos(F)=\frac{EF}{DF}$. Among the options, $\sin(F)=\frac{DE}{DF}\neq\cos(F)$, $\sin(D)=\frac{EF}{DF}=\cos(F)$, $\tan(F)=\frac{DE}{EF}\neq\cos(F)$, $\cos(D)=\frac{DE}{DF}\neq\cos(F)$. But in a right - triangle, $\sin(F)$ is the ratio of the opposite side to the hypotenuse with respect to angle $F$ and $\cos(F)$ is the ratio of the adjacent side to the hypotenuse with respect to angle $F$, so they are not equal in general.

Answer:

$\sin(F)$