Question : If $\tan \theta=\frac{8}{19}$, find the value of $\sec ^2 \theta$.
Option 1: $\frac{11}{19} \\$
Option 2: $1 \frac{8}{19} \\$
Option 3: $\frac{297}{361} \\$
Option 4: $1 \frac{64}{361}$
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Correct Answer: $1 \frac{64}{361}$
Solution :
Given: $\tan \theta=\frac{8}{19}$
We know, $\sec ^2 \theta=1+\tan^2 \theta$
$⇒\sec ^2 \theta=1+(\frac{8}{19})^2$
$⇒\sec ^2 \theta=1+\frac{64}{361}$
$⇒\sec ^2 \theta=\frac{425}{361}$
$⇒\sec ^2 \theta=1\frac{64}{361}$
Hence, the correct answer is $1\frac{64}{361}$.
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