Trigonometric Identities Question 29
Question: If an angle B is complement of an angle A, what are the greatest and least values of $ cosAcosB $ respectively?
Options:
A) $ 0,-\frac{1}{2} $
B) $ \frac{1}{2},-1 $
C) $ 1,0 $
D) $ \frac{1}{2},-\frac{1}{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
Since, A and B are complementary angles, then $ A+B=90{}^\circ $ Now, $ \cos A\cos B,=\cos A\cos (90{}^\circ -A) $ $ =\cos A\sin A=\frac{1}{2}\sin 2A $ Since, $ -1\le \sin 2A\le 1 $ Hence, $ -\frac{1}{2}\le \frac{1}{2}\sin 2A\le \frac{1}{2} $ Thus, greatest and least values of $ cosAcosB $ are $ \frac{1}{2} $ and $ -\frac{1}{2} $ .
BETA
