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If $\sin θ + \cos e c θ = 2 t h e n$ value of $\sin^{10} θ + \cos e c^{10} θ =_____$

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$2^{4}$

$2^{2}$

$2^{3}$

answer is C.

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Detailed Solution

$\sin θ + \cos e c θ = 2$
$\sin θ + \frac{1}{\sin θ} = 2$
$\sin^{2} θ - 2 \sin θ + 1 = 0$
$\sin θ = 1$
$\sin^{10} θ + \cos e c^{10} θ = 1 + 1 = 2$

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