Find the solution for given trigonometric equation $\frac{\tan 3 x - \tan 2 x}{1 + \tan 3 xtan 2 x} = 1$

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x = nπ + π / 4

solution does not exist

nπ \pm π / 4

None of these

answer is A.

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Detailed Solution

Given expression is

\frac{\tan 3 x - \tan 2 x}{1 + \tan 3 x \cdot \tan 2 x} = 1

We have,

\tan (3 x - 2 x) = 1

(since,

\tan (a - b) = \frac{\tan a - \tan b}{1 + \tan a \cdot \tan b}

)

\tan x = 1

As we know that,

\tan (x) = 1 : [\begin{matrix} Radians: & x = \frac{π}{4} + πn \\ Degrees: & x = 45^{\circ} + 180^{\circ} n \end{matrix}]

So,

x = nπ + π / 4

So, the solution of the given equation is,

x = nπ + π / 4

.
Correct option is 1.

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