Question : If $\sec \theta=2 \frac{4}{23}$,find the value of $\tan^2 \theta$.
Option 1: $2 \frac{16}{529}$
Option 2: $1 \frac{200}{529}$
Option 3: $3 \frac{384}{529}$
Option 4: $3 \frac{177}{529}$
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Correct Answer: $3 \frac{384}{529}$
Solution : Given: $\sec \theta=2 \frac{4}{23}=\frac{50}{23}$ We know, $\tan^2\theta=\sec^2\theta-1$ ⇒ $\tan^2\theta=(\frac{50}{23})^2-1$ ⇒ $\tan^2\theta=\frac{2500}{529}-1$ ⇒ $\tan^2\theta=\frac{1971}{529}$ $\therefore \tan^2\theta=3 \frac{384}{529}$ Hence, the correct answer is $3 \frac{384}{529}$.
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Question : If $\sec\theta +\tan\theta = 3$, then what is the value of $\sec \theta-\tan \theta$?
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