Trigonometric Identities Question 157
Question: What is $ \cos 20{}^\circ +\cos 100{}^\circ +\cos 140{}^\circ $ equal to?
Options:
A) 2
B) 1
C) $ 1/2 $
D) 0
Show Answer
Answer:
Correct Answer: D
Solution:
$ \cos 20{}^\circ +\cos 100{}^\circ +\cos 140{}^\circ $ $ =(\cos ,140{}^\circ +\cos 20{}^\circ )+\cos 100{}^\circ $ $ =2\cos ( \frac{160{}^\circ }{2} ).\cos ( \frac{120{}^\circ }{2} )+\cos 100{}^\circ $ $ =2.80{}^\circ .\frac{1}{2}+\cos 100{}^\circ $ $ =2\cos ( \frac{180{}^\circ }{2} ).\cos ( \frac{20{}^\circ }{2} ) $ $ =2\cos 90{}^\circ .,\cos 10{}^\circ $ $ =2\times 10\times \cos 10{}^\circ =0 $
BETA
