Trigonometric Identities Question 181
Question: The value of $ 2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1 $ is
[MP PET 1997; UPSEAT 2002]
Options:
A) 2
B) 0
C) 4
D) 6
Show Answer
Answer:
Correct Answer: B
Solution:
$ {{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{3}}={{(1)}^{3}} $
$ \Rightarrow {{\sin }^{6}}\theta +{{\cos }^{6}}\theta +3,{{\sin }^{2}}\theta ,{{\cos }^{2}}\theta =1 $ and $ {{\sin }^{4}}\theta +{{\cos }^{4}}\theta +2,{{\sin }^{2}}\theta ,{{\cos }^{2}}\theta =1 $ Both gives, $ 2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3,({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1=0 $ .
BETA
