^6 + ^6 + 3 ^2 ^2 = - Vidyadip

MCQ

${\sin ^6}\theta + {\cos ^6}\theta + 3{\sin ^2}\theta {\cos ^2}\theta = $

A
$0$
B
$-1$
✓
$1$
D
None of these

✓

Answer

Correct option: C.

$1$

c
(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 $1.$

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