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A man observe that was he has climbed up...

A man observe that was he has climbed up `1/3` of the length of an inclined ladder ,placed against a wall the angular depression of an object on the floor is `alpha` and that after he reached the top of the ledder , the angular depression `beta` If the inclintaion of the ladder to the is `theta` then prove that cot `theta=(3 cot beta-cot alpha)/2`

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To solve the problem step by step and prove that \( \cot \theta = \frac{3 \cot \beta - \cot \alpha}{2} \), we will follow these steps: ### Step 1: Understand the Setup We have a ladder inclined at an angle \( \theta \) with the ground. A man climbs up \( \frac{1}{3} \) of the length of the ladder and observes an object on the floor at an angle of depression \( \alpha \). When he reaches the top of the ladder, the angle of depression changes to \( \beta \). ### Step 2: Define Length of the Ladder Let the length of the ladder be \( L \). ...
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