A) \[b\tan \frac{1}{2}(\alpha +\beta )\]
B) \[b\tan \frac{1}{2}(\alpha -\beta )\]
C) \[a\tan \frac{1}{2}(\alpha -\beta )\]
D) None of these
Correct Answer: A
Solution :
Let Z be the length of the ladder Now, \[a+OA-OB=l\cos \beta -l\cos \alpha \] and \[b=OP-OQ=l\sin \alpha -l\sin \beta \] \[\therefore \] \[\frac{a}{b}=\frac{\cos \beta -\cos ga}{\sin \alpha -\sin \beta }\] \[\Rightarrow \]\[\frac{a}{b}=\frac{2\sin \left( \frac{\alpha +\beta }{2} \right)\sin \left( \frac{\alpha -\beta }{2} \right)}{2\cos \left( \frac{\alpha +\beta }{2} \right)\sin \left( \frac{\alpha -\beta }{2} \right)}\] \[\Rightarrow \]\[a=b\tan \left( \frac{\alpha -\beta }{2} \right)\]You need to login to perform this action.
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