Let `f(x)=log(log)_(1/3)((log)_7(sinx+a)))` be defined for every real value of `x ,` then the possible value of `a` is 3 (b) 4 (c) 5 (d) 6

Explanation

To solve the problem, we need to analyze the function \( f(x) = \log_{\frac{1}{3}}(\log_{7}(\sin x + a)) \) and determine the possible values of \( a \) such that \( f(x) \) is defined for every real value of \( x \).

### Step 1: Determine the conditions for \( f(x) \) to be defined
For \( f(x) \) to be defined, the argument of the logarithm must be positive. Therefore, we need:

\[ \log_{7}(\sin x + a) > 0 \]
...