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A train travelling on one of two interse...

A train travelling on one of two intersecting railway lines, subtends at a certain station on the other line, an/ angle `alpha` when the front of the carriage reaches the junction and an angle `beta` when the end of the carriage reaches it. Then, the two lines are inclined to each other at an angle theta, show that `2 cot theta=cot alpha-cot beta cot alpha + cot beta`

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A train travelling on one of two intersecting railway lines, subtends at a certain station on the other line, an angle alpha when the front of the carriage reaches the junction, and an angle beta when the end of the carriage reaches it. Prove that the two lines are inclined to each other at an angle theta determined by 2cot theta = cot alpha - cot beta .

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