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If tan θ = 4/3, calculate sin\(^2\) θ - cos\(^2\) θ.

Mathematics
JAMB 2002

If tan θ = 4/3, calculate sin\(^2\) θ - cos\(^2\) θ.

  • A. 16/25
  • B. 24/25
  • C. 7/25
  • D. 9/25
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Correct Answer: Option C
Explanation

\(\tan \theta = \frac{opposite}{adjacent} = \frac{4}{3}\)

Hyp\(^2\) = 4\(^2\) + 3\(^2\)

Hyp = 5.

\(\sin \theta = \frac{4}{5}; \cos \theta = \frac{3}{5}\)

\(\sin^{2} \theta - \cos^{2} \theta = \frac{16}{25} - \frac{9}{25}\)

= \(\frac{7}{25}\)


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