Solve for `x :` `2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2`

Explanation

To solve the equation \( 2\tan^{-1}(\sin x) = \tan^{-1}(2\sec x) \), we will follow these steps:

### Step 1: Use the double angle formula for tangent
We can use the formula for \( 2\tan^{-1}(y) \):
\[ 2\tan^{-1}(y) = \tan^{-1}\left(\frac{2y}{1-y^2}\right) \]
In our case, let \( y = \sin x \). Thus, we have:
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