If ${sin}^{2} (3 x + 45) + {cos}^{2} (2 x + 60) = 1$ then $x =$ __________.

60

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30

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15

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0

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Solution

The correct option is C $15$
${sin}^{2} (3 x + 45) + {cos}^{2} (2 x + 60) = 1$
but by identity, we have
${sin}^{2} θ + {cos}^{2} θ = 1,$
$∴ 3 x + 45 = 2 x + 60$
$∴ x = 15$

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