If $sin x + {sin}^{2} x = 1$ , then the value of expression ${cos}^{12} x + 3 {cos}^{10} x + 3 {cos}^{8} x + {cos}^{6} x - 1$ is equal to

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Solution

The correct option is A \N
Since $s i n x + s i n^{2} x = 1, \Rightarrow s i n x = 1 - s i n^{2} x = c o s^{2} x . . . . . (i)$
The given expression is
$= c o s^{6} x (c o s^{6} x + 3 c o s^{4} x + 3 c o s^{2} x + 1) - 1 = c o s^{6} x (c o s^{2} x + 1)^{3} - 1, (∵ s i n x = c o s^{2} x) = (s i n^{2} x + s i n x)^{3} - 1 = 1 - 1 = 0$

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Similar questions

If sinx + $s i n^{2} x$ = 1 Then the value of $c o s^{12} x + 3 c o s^{10} x + 3 c o s^{8} x + c o s^{6} x$ is equal to

$I f s i n x + s i n^{2} x = 1, t h e n t h e v a l u e o f c o s^{12} x + 3 c o s^{10} x + 3 c o s^{8} x + c o s^{6} x - 1 i s e q u a l t o$

sin x + {sin}^{2} x = 1

{cos}^{12} x + 3 {cos}^{10} x + 3 {cos}^{8} x + {cos}^{6} x + 2 {cos}^{4} x + {cos}^{2} x - 2 =

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