Given that sin \(P = \frac{5}{13}\), where p is acute, find the value of cos p - tan p
A
\(\frac{79}{156}\)
B
\(\frac{85}{156}\)
C
\(\frac{7}{13}\)
D
\(\frac{8}{1}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
If \(sin P = \frac{5}{13}\) from right angled triangle from Pythagoras theorem
\(BC^2 = 13^2 - 5^2\)
= 169 - 25
BC = \(\sqrt{144}\) = 12
∴ cos P - tan P = \(\frac{12}{13} - \frac{5}{12}\)
=\(\frac{79}{156}\)
Source: Myschool Past Questions Archive (Record #26498)