If `b >1,sint >0,cost >0a n d(log)_b(sint)=x ,t h e n(log)_b(cost)` is equal to `1/2(log)_b(a-b^(2x))` (b) `2log(1-b^(x/2))` `(log)_bsqrt(1-b^(2x))` (d) `sqrt(1-x^2)`

Explanation

To solve the problem, we need to find the value of \( \log_b(\cos t) \) given that \( \log_b(\sin t) = x \).

### Step-by-Step Solution:

1. **Use the property of logarithms**:
Given \( \log_b(\sin t) = x \), we can rewrite this in exponential form:
\[
\sin t = b^x
...