Question : If $\sec \theta+\tan \theta=3$, then the value of $\sec \theta$ is:
Option 1: $\frac{4}{3}$
Option 2: $\frac{3}{4}$
Option 3: $\frac{3}{5}$
Option 4: $\frac{5}{3}$
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Correct Answer: $\frac{5}{3}$
Solution :
Given: The value of the trigonometric equation is $\sec \theta+\tan \theta=3$.
We know that if $\sec \theta+\tan \theta=x$. Then, $\sec \theta–\tan \theta=\frac{1}{x}$.
$\sec \theta+\tan \theta=3$ (equation 1)
⇒ $\sec \theta–\tan \theta=\frac{1}{3}$ (equation 2)
Adding equation 1 and equation 2,
$\sec \theta+\tan \theta+\sec \theta–\tan \theta=3+\frac{1}{3}$
⇒ $2\sec \theta=\frac{3\times 3 +1}{3}$
⇒ $2\sec \theta=\frac{10}{3}$
⇒ $\sec \theta=\frac{5}{3}$
Hence, the correct answer is $\frac{5}{3}$.
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