Question : If $\sec\theta+\tan\theta=2$, then the value of $\sec\theta$ is:
Option 1: $\frac{4}{5}$
Option 2: $5$
Option 3: $\frac{5}{4}$
Option 4: $\sqrt{2}$
Correct Answer: $\frac{5}{4}$
Solution :
Given: $\sec\theta+\tan\theta=2$ -----(1)
We know, $\sec^2\theta-\tan^2\theta=1$
Or, $(\sec\theta+\tan\theta)(\sec\theta-\tan\theta)=1$
$\therefore (\sec\theta-\tan\theta)=\frac{1}{2}$ ------(2)
Solving equations 1 and 2, we get,
$2\sec\theta=2 +\frac{1}{2}=\frac{5}{2}$
$\therefore \sec\theta=\frac{5}{4}$
Hence, the correct answer is $\frac{5}{4}$.
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