Question
Tue May 08, 2012 By: Ankita Patel
 

Solve the equation: (tan^(-1)x)^(2)+ (cot^(-1)x)^(2)=5II^(2)/8

Expert Reply
Fri May 11, 2012
Let x= tan?
therefore tan-1x =?
and cot-1x = cot-1tan? =  cot-1cot(?/2-?)= ?/2-?
Putting this value in the eqn, we get
?2+(?/2-?)2=5?2/8
8?2+8(?/2-?)2=5?2
8?2+8(?2/4 + ?- ??)=5?2
8?2+2?2 + 8?- 8??=5?2
16?- 8??-3?2=0
This quadratic eqn has roots as
?=8?±16?/32 = -?/4 and 3?/4
 
so x = tan? = tan(-?/4) = tan3?/4 = -1
 
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