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3.Trigonometrical Ratios, Functions and Identities
easy
The value of $2({\sin ^6}\theta + {\cos ^6}\theta ) - 3({\sin ^4}\theta + {\cos ^4}\theta ) + 1$ is
A
$2$
B
$0$
C
$4$
D
$6$
Solution
(b) ${({\sin ^2}\theta + {\cos ^2}\theta )^3} = {(1)^3}$
$ \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, $2\,\,({\sin ^6}\theta + {\cos ^6}\theta ) – 3\,({\sin ^4}\theta + {\cos ^4}\theta ) + 1 = 0$.
Standard 11
Mathematics
