Show that \(\frac{\sin 2x}{1 + \cos x}\) + \(\frac{sin2 x}{1 - cos x}\) is
A
sin x
B
cos2x
C
2
D
3
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{\sin^{2} x}{1 + \cos x} + \frac{\sin^{2} x}{1 - \cos x}\)
\(\frac{\sin^{2} x (1 - \cos x) + \sin^{2} x (1 + \cos x)}{1 - \cos^{2} x}\)
= \(\frac{\sin^{2} x - \cos x \sin^{2} x + \sin^{2} x + \sin^{2} x \cos x}{\sin^{2} x}\)
(Note: \(\sin^{2} x + \cos^{2} x = 1\)).
= \(\frac{2 \sin^{2} x}{\sin^{2} x}\)
= 2.
Source: Myschool Past Questions Archive (Record #32594)