If tan \theta = 4/3, calculate sin\(^2\) \theta - cos\(^2\) \theta.
A
16/25
B
24/25
C
7/25
D
9/25
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\tan \theta = \frac{opposite}{adjacent} = \frac{4}{3}\)
Hyp\(^2\) = 4\(^2\) + 3\(^2\)
Hyp = 5.
\(\sin \theta = \frac{4}{5}; \cos \theta = \frac{3}{5}\)
\(\sin^{2} \theta - \cos^{2} \theta = \frac{16}{25} - \frac{9}{25}\)
= \(\frac{7}{25}\)
Source: Myschool Past Questions Archive (Record #3375)