If tan x = \(\frac{4}{3}\), 0\(^o\) < x < 90\(^o\), find the value of sin x - cos x

  • A \(\frac{1}{10}\)
  • B \(\frac{1}{5}\)
  • C \(\frac{5}{12}\)
  • D 1\(\frac{2}{5}\)
waec 2018mathematics

The correct answer is B. \(\frac{1}{5}\)

From the diagram,

h\(^2\) = 4\(^2\) + 3\(^2\) (pythagoras')

h\(^2\) = 16 + 9 = 25

h = \(\sqrt{25}\) = 5

Hence, sin x - cos x

= \(\frac{4}{5} - \frac{3}{5}\)

= \(\frac{2}{5}\)

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