Question

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

Explanation:

Step1: Determine the angles of \(\triangle DEF\)

Since \(DE = EF=5\) and \(DF = 5\sqrt{2}\), by Pythagoras theorem \(DE^{2}+EF^{2}=5^{2}+5^{2}=25 + 25=50=(5\sqrt{2})^{2}=DF^{2}\), so \(\angle E = 90^{\circ}\). And since \(DE = EF\), \(\angle D=\angle F = 45^{\circ}\).

Step2: Calculate the trigonometric values

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

Answer:

\(\tan(F)\)