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

Asked by Ankita Patel | 8th May, 2012, 09:09: PM

Expert Answer:

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
 

Answered by  | 11th May, 2012, 10:36: PM

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