Answer:
D
Step-by-step explanation:
Using the trigonometric identity
• tan²x + 1 = sec²x
tanx = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{5}{7}[/tex], thus
sec²x = ([tex]\frac{5}{7}[/tex])² + 1
= [tex]\frac{25}{49}[/tex] + [tex]\frac{49}{49}[/tex] = [tex]\frac{74}{49}[/tex]
Take the square root of both sides
secx = [tex]\sqrt{\frac{74}{49} }[/tex] = [tex]\frac{\sqrt{74} }{7}[/tex] → D
