The general solution of the equation `tan(x+20^@)tan(x-4 0^(@))=tan(x-2 0^(@))tan(x+4 0^(@))` is

Options

A. (a) `x = npi, n in Z`
B. (b) `x = npi + pi/4, n in Z`
C. (c) `x = (npi)/2, n in Z`
D. (d) `x = 2npi + pi/4, n in Z`

Explanation

To solve the equation \( \tan(x + 20^\circ) \tan(x - 40^\circ) = \tan(x - 20^\circ) \tan(x + 40^\circ) \), we will follow these steps:

### Step 1: Rewrite the equation using sine and cosine
We know that \( \tan \theta = \frac{\sin \theta}{\cos \theta} \). Therefore, we can rewrite the equation as:
\[ \frac{\sin(x + 20^\circ)}{\cos(x + 20^\circ)} \cdot \frac{\sin(x - 40^\circ)}{\cos(x - 40^\circ)} = \frac{\sin(x - 20^\circ)}{\cos(x - 20^\circ)} \cdot \frac{\sin(x + 40^\circ)}{\cos(x + 40^\circ)} \]

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