The number of solutions of the equation `cos6x+tan^2x+cos(6x)tan^2x=1` in the interval `[0,2pi]` is (a)`4` (b)` 5` (c) `6` (d) `7`

Explanation

To find the number of solutions of the equation \( \cos(6x) + \tan^2(x) + \cos(6x) \tan^2(x) = 1 \) in the interval \( [0, 2\pi] \), we can follow these steps:

### Step 1: Rewrite the Equation
Start by rewriting the equation:
\[ \cos(6x) + \tan^2(x) + \cos(6x) \tan^2(x) = 1 \]
We can factor out \( \cos(6x) \):
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