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Given that sin \(P = \frac{5}{13}\), where p is acute, find the value of cos...

Mathematics
WAEC 2001

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. \(\frac{8}{1}\)
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Correct Answer: Option A
Explanation

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 = \(\frac{12}{13} - \frac{5}{12}\)
=\(\frac{79}{156}\)


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