If $S i n x + S i n^{2} x = 1$ the $C o s^{8} x + 2 C o s^{6} x + C o s^{4} x = . . . . . . .$

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Solution

The correct option is D $1$
$s i n x = 1 - s i n^{2} x$
$s i n x = c o s^{2} x$
$(c o s^{2} x)^{4} + 2 (c o s^{2} x)^{3} + (c o s^{2} x)^{2}$
$\equiv (s i n x)^{4} + 2 (s i n x)^{3} + (s i n x)^{2}$
$\equiv s i n^{2} x (s i n x + 1)^{2}$
$\equiv (1 - s i n x) (1 + s i n x) (1 + s i n x)$
$\equiv (1 - s i n^{2} x) (1 + s i n x)$
$\equiv (s i n x) (1 + s i n x)$
$\equiv s i n x + s i n^{2} x$
$\equiv 1$

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Similar questions

s i n x + s i n^{2} x = 1

c o s^{8} x + 2 c o s^{6} x + c o s^{4} x

If $s i n x + s i n^{2} x = 1$ , then write the value of $c o s^{8} x + 2 c o s^{6} x + c o s^{4} x .$

s i n x + s i n^{2} x = 1

{c o s}^{2} x + {c o s}^{4} x = 1

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

{cos}^{2} x + {cos}^{4} x = 1

s i n x + s i n^{2} x = 1

c o s^{2} x + c o s^{4} x

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