If `sin(x+20^0)=2sinxcos40^0,where in (0,pi/2),` then which of the following hold(s) good? (a)`cos2x=1/2` (b) `cos e c4x=2` (c)`secx/2=sqrt(6)-sqrt(2)` (d) `tanx/2=(2-sqrt(3))`

Explanation

To solve the equation \( \sin(x + 20^\circ) = 2 \sin x \cos 40^\circ \) where \( x \in (0, \frac{\pi}{2}) \), we will follow these steps:

### Step 1: Use the sine addition formula
We can express \( \sin(x + 20^\circ) \) using the sine addition formula:
\[ \sin(x + 20^\circ) = \sin x \cos 20^\circ + \cos x \sin 20^\circ \]
Thus, we rewrite the equation as:
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