A) \[\tan \theta \]
B) \[\cot \theta \]
C) \[\cot 2\theta \]
D) \[\sin 2\theta \]
Correct Answer: C
Solution :
Slope at \[{{T}_{2}}>\] Slope at \[{{T}_{1}}\]. So \[{{R}_{2}}<{{R}_{1}}\]. \[{{R}_{2}}={{R}_{0}}(1+\alpha {{T}_{2}})\] \[{{R}_{1}}={{R}_{0}}(1+\alpha {{T}_{1}})\] Subtracting, we get, \[{{R}_{0}}\alpha ({{T}_{2}}-{{T}_{1}})={{R}_{2}}-{{R}_{1}}\] \[{{T}_{2}}-{{T}_{1}}=\cot ({{90}^{0}}-\theta )-\cot \theta \] \[=\tan \theta -\cot \theta \] \[{{T}_{2}}-{{T}_{1}}=\frac{{{\sin }^{2}}\theta -{{\cos }^{2}}\theta }{\sin \theta \cos \theta }=\frac{-2\cos 2\theta }{\sin 2\theta }\] or \[{{T}_{1}}-{{T}_{2}}=2\,\cot \,2\theta \]
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