cot A-1 2-sec? A cot A 1 + tan A
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cot A-1 2-sec? A cot A 1 + tan A

JEE/Engineering Exams
Maths
Solution
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( begin{aligned} & text { LHS } =frac{cot A-1}{2-sec ^{2} A} &=frac{1-tan A}{tan Aleft(2-1-tan ^{2} Aright)} =& frac{1-tan A}{tan Aleft(1-tan ^{2} Aright)} =& frac{1-tan A}{tan A(1-tan A)(1+tan A)} =& frac{1}{tan A(1+tan A)} =& frac{cot A}{1+tan A} =& operatorname{Rr} S end{aligned} ) Vever, proved.
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