A body cools in a surrounding which is at a constant temperature of `theta_(0)` Assume that it obeys Newton's law of cooling Its temperature `theta` is plotted against time t Tangents are drawn to the curve at the points `P (theta =theta_(1))` and `Q(theta =theta_(2))` These tangents meet the time axis at angle of `phi_(2)` and`phi_(1)` as shown
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Explanation

Temperature as a function of time is given as
` T_(1)-T_(0))e^(-kt)`
Slope of curve is
`(dT)/(dt) = -k(T_(1)-T_(0)) e^(-kt) = -k(T-T_(0)`
if at `T = T_(1)` slope is `tan theta_(1)`, we use
`tan theta_(1) = -k(T_(1)-T_(0))` …(1)
and at `T = T_(2)` slope is `tan theta _(2)`, we use
`tan theta_(2) = -k(T_(2)-T_(0))` ...(2)
`((2))/((1))` gives
`(tan theta_(2))/(tan theta_(1)) = (T_(2)-T_(0))/(T_(1)-T_(0))`