Given that tan x = 5/12, what is the value of sin x + cos x ?

  • A 5/13
  • B 7/13
  • C 12/13
  • D 17/13
  • E 5/12
waec 1993mathematics

The correct answer is D. 17/13

\(\tan x = \frac{opp}{adj} = \frac{5}{12}\)

\(Hyp^2 = opp^2 + adj^2\)

\(Hyp^2 = 5^2 + 12^2\)

= \(25 + 144 = 169\)

\(Hyp = \sqrt{169} = 13\)

\(\sin x = \frac{5}{13}; \cos x = \frac{12}{13}\)

\(\sin x + \cos x = \frac{5}{13} + \frac{12}{13}\)

= \(\frac{17}{13}\)

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