If sin x = 12/13, where 0^\circ < x < 90^\circ, find the value of 1 - cos\(^2\)x
A
25/169
B
64/169
C
105/169
D
144/169
E
8/13
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\sin x = \frac{12}{13}\)
\(\cos x = \frac{5}{13}\)
\(\cos^{2} x = (\frac{5}{13})^2 = \frac{25}{169}\)
\(1 - \cos^{2} x = 1 - \frac{25}{169}\)
= \(\frac{144}{169}\)
Source: Myschool Past Questions Archive (Record #23219)