Question

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

Explanation:

Step1: Identify triangle type

$\triangle DEF$ is isosceles right triangle, $\angle E=90^\circ$, $DE=EF=5$, $\angle D=\angle F=45^\circ$

Step2: Calculate $\cos(F)$

$\cos(45^\circ)=\frac{\sqrt{2}}{2}$

Step3: Evaluate each option

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

Answer:

tan(F).