Question

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

triangle def: d and f are on the base, length 6√2. ed and ef are both 5, angle at e is the vertex.

Explanation:

Step1: Verify triangle type

Check if $\triangle DEF$ is right-angled:
$$5^2 + 5^2 = 25 + 25 = 50$$
$$(5\sqrt{2})^2 = 25 \times 2 = 50$$
Since $DE^2 + EF^2 = DF^2$, $\angle E = 90^\circ$, and $DE=EF=5$, so $\angle D = \angle F = 45^\circ$.

Step2: Calculate trigonometric values

• $\cos(F) = \cos(45^\circ) = \frac{\sqrt{2}}{2}$
• $\sin(F) = \sin(45^\circ) = \frac{\sqrt{2}}{2}$
• $\sin(D) = \sin(45^\circ) = \frac{\sqrt{2}}{2}$
• $\tan(F) = \tan(45^\circ) = 1$
• $\cos(D) = \cos(45^\circ) = \frac{\sqrt{2}}{2}$

Step3: Identify non-equal value

Compare all values to $\cos(F)$; only $\tan(F)$ does not match.

Answer:

tan(F)