Trigonometric Identities Question 186
Question: If $ \sin x+{{\sin }^{2}}x=1, $ then $ {{\cos }^{8}}x+2{{\cos }^{6}}x+{{\cos }^{4}}x= $
Options:
A) 0
B) -1
C) 2
D) 1
Show Answer
Answer:
Correct Answer: D
Solution:
We have $ \sin x+{{\sin }^{2}}x=1\Rightarrow \sin x={{\cos }^{2}}x $ \ $ {{\cos }^{8}}x+2{{\cos }^{6}}x+{{\cos }^{4}}x={{\sin }^{4}}x+2{{\sin }^{3}}x+{{\sin }^{2}}x $ $ ={{(\sin x+{{\sin }^{2}}x)}^{2}}=1 $ .
BETA
