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If tanx = 4/3, 0° < x <90°, find the value of sinx - cosx

A: 1/10

B: 1/5

C: 5/12

D: 1 2/5

**Comments**

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tanx = opp/adj = 4/3

sinx = opp/hyp ------------- eqn(1)

cosx = adj/hyp -------------- eqn(2)

From pythagoras theorem, hyp^{2} = opp^{2} + adj^{2}

opp = 4

adj = 3

hyp^{2} = 4^{2} + 3^{2}

hyp = √(4^{2} + 3^{2})

hyp = √(16 + 9)

hyp = √(25)

hyp = 5

from eqn(1), sinx = 4/5

from eqn(2), cosx = 3/5

Thus, sinx - cosx = 4/5 - 3/5

= 1/5

**Answer: B**

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