A man observes when 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 `alphadot` When he climbs the ladder completely, the angleof depression is `beta` . If the inclination of the ladder to the floor is `theta,` then prove that `cottheta=(3cotbeta-cotalpha)/2`

Explanation

`sinntheta=(DM)/(1/3l)`

`DM=1/3lsintheta`

`Sintheta=(BC)/l`

`BC=lsintheta`

`cotalpha=(OM)/(DM)`

`OM=1/3lsinthetacotalpha`

`Cot beta=(OC)/(BC)`

`OC=lsinthetacotbeta`

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