Tasty Logarithm #4

Geometry Level 3

logsin(x)cos(x)+logcos(x)sin(x)=2\large \log_{\sin(x)} \cos (x) +\log_{\cos(x)} \sin(x) =2

If the minimum value of xx that satisfy the equation above is equals to πa\dfrac{\pi}{a} for some constant aa, find the value of aa.

Give your answer to 3 decimal places.

Note: Angles are measured in radians.

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