Question:
The general solution of the equation \(\tan^2x=1\) is
The general solution of the equation \(\tan^2x=1\) is
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When \(\tan x=\pm 1\), the general solution is \(x=n\pi\pm\frac{\pi}{4}\).
Updated On: May 7, 2026
- \(n\pi+\frac{\pi}{4}\) only
- \(n\pi\pm\frac{\pi}{4}\)
- \(2n\pi\pm\frac{\pi}{4}\)
- \(n\pi-\frac{\pi}{4}\) only
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The Correct Option is B
Solution and Explanation
Step 1: Given, \[ \tan^2x=1 \]
Step 2: Taking square root: \[ \tan x=\pm 1 \]
Step 3: We know: \[ \tan\frac{\pi}{4}=1 \] and \[ \tan\left(-\frac{\pi}{4}\right)=-1 \]
Step 4: Since \(\tan x\) has period \(\pi\), the general solution is: \[ x=n\pi\pm\frac{\pi}{4} \] \[ \boxed{n\pi\pm\frac{\pi}{4}} \]
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