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If tanx = 4/3, 0° < x <90°, find the value of ...
waec-2018 ssce-exam-2018 math waec-mathematics-2018
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If tanx = 4/3, 0° < x <90°, find the value of sinx - cos⁡x

A:  1/10

B:  1/5

C:  5/12

D:  1 2/5

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alberteinstein
Asked by alberteinsteinrep:269
School not set Nigeria
31 August 2020

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peter
Peter answeredrep:1.7K
University of Lagos Nigeria
01 September 2020
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tanx = opp/adj = 4/3

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

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

From pythagoras theorem, hyp2 = opp2 + adj2

opp = 4

adj = 3

hyp2 = 42 + 32

hyp = √(42 + 32)

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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