Show that (frac{sin 2x}{1 + cos x}) + (frac{sin2 x}{1 – cos x}) is
-
A.
sin x -
B.
cos2x -
C.
2 -
D.
3
Correct Answer: Option C
Explanation
(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.