Question : If $\sin \mathrm{C}=\frac{9}{10}$, then what is the value of $\cos ^2 \mathrm{C}$?
Option 1: $\frac{19}{100}$
Option 2: $\frac{81}{\sqrt{19}}$
Option 3: $\frac{19}{10}$
Option 4: $\frac{\sqrt{19}}{100}$
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Correct Answer: $\frac{19}{100}$
Solution :
We know,
$\sin^2 \mathrm{C} + \cos^2 \mathrm{C} = 1$
$⇒\cos^2 \mathrm{C} = 1 - \sin^2 \mathrm{C}$
Substituting $\sin \mathrm{C} = \frac{9}{10}$,
$⇒\cos^2 \mathrm{C} = 1 - \left(\frac{9}{10}\right)^2 = 1 - \frac{81}{100} = \frac{19}{100}$
Hence, the correct answer is $ \frac{19}{100}$.
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