If $sin x + {sin}^{2} x = 1$ , then the value of ${cos}^{2} x + {cos}^{4} x$ is equal to

1

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\frac{1}{2}

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\frac{1}{3 \sqrt{3}}

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\frac{3 \sqrt{5} - 5}{2}

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Solution

The correct option is D $1$
Given, $sin x + {sin}^{2} x = 1$
We need to find a value of ${cos}^{2} x + {cos}^{4} x$
Therefore, ${cos}^{2} x + {cos}^{4} x = 1 - {sin}^{2} x + (1 - {sin}^{2} x)^{2}$ [Using $1 - s i n^{2} x = c o s^{2} x$ ]
$⟹ {cos}^{2} x + {cos}^{4} x = 1 - {sin}^{2} x + (sin x)^{2}$ [Using $sin x +$ $sin$ $^{2}$ $x$ $= 1$ ]
$⟹ {cos}^{2} x + {cos}^{4} x = 1$

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Similar questions

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

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

If $\frac{s i n^{4} x}{2} + \frac{c o s^{4} x}{3} = \frac{1}{5}$ , then

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

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

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