Question : If $3 x=\sec A$ and $\frac{3}{x}=\tan A$, then $9\left(x^2-\frac{1}{x^2}\right)$ is:
Option 1: $3$
Option 2: $9$
Option 3: $1$
Option 4: $\frac{1}{9}$
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Answer (1)
22nd Jan, 2024
Correct Answer: $1$
Solution :
We know that,
$\sec ^2A-\tan^2 A=1$
⇒ $(3x)^2-(\frac{3}{x})^2=1$
⇒ $9x^2-\frac{9}{x^2}=1$
⇒ $9\left(x^2-\frac{1}{x^2}\right)=1$
Hence, the correct answer is $1$.
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