If `asinx+bcos(x+theta)+bcos(x-theta)=d ,` then the minimum value of `|costheta|` is equal to (a)`1/(2|b|)sqrt(d^2-a^2)` (b) `1/(2|a|)sqrt(d^2-a^2)` (c)`1/(2|d|)sqrt(d^2-a^2)` (d) none of these

Explanation

To solve the equation \( a \sin x + b \cos(x + \theta) + b \cos(x - \theta) = d \) and find the minimum value of \( |\cos \theta| \), we can follow these steps:

### Step 1: Simplify the given equation
We start with the equation:
\[ a \sin x + b \cos(x + \theta) + b \cos(x - \theta) = d \]
Using the cosine addition formula, we can rewrite \( \cos(x + \theta) \) and \( \cos(x - \theta) \):
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