Trigonometric Identities Question 242
Question: The value of $ 6({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-9({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+4 $ is
[MP PET 2001]
Options:
A) -3
B) 0
C) 1
D) 3
Show Answer
Answer:
Correct Answer: C
Solution:
$ 6({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-9({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+4 $ $ =6[{{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{3}}-3{{\sin }^{2}}\theta {{\cos }^{2}}\theta ({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )] $ $ -9[{{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{2}}-2{{\sin }^{2}}\theta {{\cos }^{2}}]+4 $ $ =6[1-3{{\sin }^{2}}\theta {{\cos }^{2}}\theta ]-9,[1-2{{\sin }^{2}}\theta {{\cos }^{2}}\theta ]+4 $ $ =6-9+4=1 $ .
BETA
