In the coaxial system of circles, if the common tangent of two circles subtend angles $\theta_{1}$ and $\theta_{2}$ at the limiting points then the value of $\cos(\theta_{1}+\theta_{2})=$

For a coaxial system of circles, the limiting points lie on the common tangent at the exact point of tangency. This means both angles theta 1 and theta 2 are formed at the same point on the line, making the rays coincide. Adding the two subtended angles at this single point of tangency results in a total angle of 180 degrees or pi radians. Therefore, the cosine of theta 1 plus theta 2 is the cosine of 180 degrees, which equals negative 1.

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