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
\(\frac{8}{1}\)
Explanation
Correct Option
a
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Silentgeez
1 year ago
Given that sin P = 5/13, we can find cos P using the Pythagorean identity: cos P = √(1 - sin^2 P) = √(1 - (5/13)^2) = √(1 - 25/169) = √(144/169) = 12/13.
Next, we can find tan P using the definition of tangent: tan P = sin P / cos P = (5/13) / (12/13) = 5/12.
Therefore, cos P - tan P = (12/13) - (5/12) = (144/169) - (65/169) = 79/169.
