A) \[{{m}^{2}}-{{n}^{2}}=4mn\]
B) \[{{m}^{2}}+{{n}^{2}}=4mn\]
C) \[{{m}^{2}}-{{n}^{2}}={{m}^{2}}+{{n}^{2}}\]
D) \[{{m}^{2}}-{{n}^{2}}=4\sqrt{mn}\]
Correct Answer: D
Solution :
[d]: Clearly, \[(m+n)=2tan\theta \] and \[(m-n)=2\sin \theta \] \[\therefore \]\[{{m}^{2}}-{{n}^{2}}=4\tan \theta .\sin \theta \] ...(i) Also,\[4\sqrt{mn}=4\sqrt{{{\tan }^{2}}\theta -{{\sin }^{2}}\theta }=4\sin \theta .tan\theta \]...(ii) From (i) and (ii), \[{{m}^{2}}-{{n}^{2}}=4\sqrt{mn}\]
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