1 10. 1 -A 30000 - Cos A + cos B - ...
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1 10. 1 -A 30000 - Cos A + cos B - cos(A + B) 1 + cos A - cos B - cos(A + B) = tan

JEE/Engineering Exams
Maths
Solution
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( frac{1-cos A+cos B-cos (A+B)}{1+cos A-cos B-cos (A+B)} ) ( =frac{2 sin ^{2} A+2 sin (A+2 B) sin frac{A}{2}}{2 cos ^{2} A-2 cos left(frac{A+2 B}{2}right) cos frac{A}{2}} ) ( =tan left(frac{A}{2}right) cdotleft(frac{sin left(frac{A}{2}right)+sin left(frac{A+2 B}{2}right)}{cos left(frac{A}{2}right)-cos (A+2 B)}right) ) ( =tan frac{A}{2} cdot frac{2 sin (A+B) cos left(frac{B}{2}right)}{2 sin left(frac{B}{2}right) sin left(frac{A+B}{2}right)} ) ( =tan left(frac{A}{2}right) cdot cot left(frac{B}{2}right) )
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