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The value of $\sin^{2} 30 ° \div \sin^{2} 45 °$ is

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By Expert Faculty of Sri Chaitanya

a

2

b

\frac{1}{2}

c

\sqrt{3}

d

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

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detailed solution

Correct option is B

$\begin{array}{l} \sin^{2} 30 ° = {(\frac{1}{2})}^{2} = \frac{1}{4} \\ \sin^{2} 45 ° = {(\frac{1}{\sqrt{2}})}^{2} = \frac{1}{2} \\ ∴ \sin^{2} 30 ° \div \sin^{2} 45 ° = \frac{1}{4} \div \frac{1}{2} \\ = \frac{(\frac{1}{4})}{(\frac{1}{2})} = \frac{1}{4} \times \frac{2}{1} = \frac{1}{2} \end{array}$

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