Answer:
B
Step-by-step explanation:
By the definition,
[tex]\sec \theta=\dfrac{\text{hypotenuse}}{\text{adjacent leg}}.[/tex]
If [tex]\sec \theta=\dfrac{25}{24},[/tex] we can consider right triangle with hypotenuse 25 un. and adjacent leg 24 un. By the Pythagorean theorem,
[tex]\text{hypotenuse}^2=\text{adjacent leg}^2+\text{opposite leg}^2,\\ \\\text{opposite leg}^2=25^2-24^2,\\ \\\text{opposite leg}^2=625-576,\\ \\\text{opposite leg}^2=49,\\ \\\text{opposite leg}=7\ un.[/tex]
So,
[tex]\cot \theta=\dfrac{\text{adjacent leg}}{\text{opposite leg}}=\dfrac{24}{7}.[/tex]
