- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
easy
${\sin ^6}\theta + {\cos ^6}\theta + 3{\sin ^2}\theta {\cos ^2}\theta = $
A
$0$
B
$-1$
C
$1$
D
None of these
Solution
(c) ${\sin ^6}\theta + {\cos ^6}\theta + 3\,{\sin ^2}\theta \,{\cos ^2}\theta $
$ = {({\sin ^2}\theta + {\cos ^2}\theta )^3} – 3{\sin ^2}\theta {\cos ^2}\theta + 3{\sin ^2}\theta {\cos ^2}\theta = 1.$
Trick : Put $\theta = {0^o},$
we get the value of expression equal to $1. $
Again put $\theta = {45^o},$ the value remains $1,$ it means that the expression is independent of $\theta$ and is equal to $1.$
Standard 11
Mathematics
