Question

given (\triangle 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 \(\angle E=90^{\circ}\), \(\angle D=\angle F = 45^{\circ}\) (isosceles right - triangle).

Step2: Calculate the trigonometric values

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

So, \(\tan(F)\) is not equal to \(\cos(F)\).

Answer:

\(\tan(F)\)