The general solution of the equation ${tan}^{2} x = 1$ is

n π + \frac{π}{4}

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n π - \frac{π}{4}

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n π \pm \frac{π}{4}

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2 n π \pm \frac{π}{4}

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Solution

The correct option is B $n π \pm \frac{π}{4}$
${tan}^{2} x = 1$ ..... $(i)$
$⟹ tan x = \pm 1$
$⟹ x = {tan}^{- 1} (\pm 1)$
Now, $x = {tan}^{- 1} (1) = n π + \frac{π}{4}$ in general
Also, $x = {tan}^{- 1} (- 1) = n π - \frac{π}{4}$ in general
$∴ {tan}^{- 1} (\pm 1) = n π \pm \frac{π}{4}$ in general
Thus, $x = n π \pm \frac{π}{4}$ is the general solution of $(i)$

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The general solution of the equation tan2x=1 is

The correct option is B nπ±π4tan2x=1 ..... (i)⟹tanx=±1⟹x=tan−1(±1)Now, x=tan−1(1)=nπ+π4 in generalAlso, x=tan−1(−1)=nπ−π4 in general∴tan−1(±1)=nπ±π4 in generalThus, x=nπ±π4 is the general solution of (i)

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