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

Explanation

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

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

Hyp = 5.

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

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

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