Trigonometric Identities Question 41
Question: Value of $ 2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta ) $ $ -3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1 $ is
Options:
A) 2
B) 0
C) 4
D) 6
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ 2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1 $ $ =2[{{({{\sin }^{2}}\theta )}^{3}}+{{({{\cos }^{2}}\theta )}^{3}}]-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1 $ $ =2[({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )({{\sin }^{4}}\theta +{{\cos }^{4}}\theta -{{\sin }^{2}}\theta $ $ {{\cos }^{2}}\theta )]-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1 $ $ =[2{{\sin }^{4}}\theta +2{{\cos }^{4}}\theta -2{{\sin }^{2}}\theta {{\cos }^{2}}\theta ]-3{{\sin }^{4}}\theta -3{{\cos }^{4}}\theta +1 $ $ =-{{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{2}}+1=-1^{2}+1=-1+1=0 $
BETA
