Simplify: ((1 – sin theta)(1 + sin theta)).
-
A.
(sin^{2} theta) -
B.
(sec^{2} theta) -
C.
(tan^{2} theta) -
D.
(cos^{2} theta)
Correct Answer: Option D
Explanation
((1 + sin theta)(1 – sin theta) = 1 – sin theta + sin theta – sin^{2} theta)
(= 1 – sin^{2} theta)
Recall, (cos^{2} theta + sin^{2} theta = 1)
(therefore 1 – sin^{2} theta = cos^{2} theta).