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 angles of \[{{\varphi }_{2}}\]and \[{{\varphi }_{1}}\], as shown

• A. \[\frac{\tan \,{{\varphi }_{2}}}{\tan \,{{\varphi }_{1}}}=\frac{{{\theta }_{1}}-{{\theta }_{0}}}{{{\theta }_{2}}-{{\theta }_{0}}}\]   
• B. \[\frac{\tan \,{{\varphi }_{2}}}{\tan \,{{\varphi }_{1}}}=\frac{{{\theta }_{2}}-{{\theta }_{0}}}{{{\theta }_{1}}-{{\theta }_{0}}}\]
• C. If assertion is true but reason is false.
• D. \[\frac{\tan \,{{\varphi }_{1}}}{\tan \,{{\varphi }_{2}}}=\frac{{{\theta }_{2}}}{{{\theta }_{1}}}\]