Q)

Asked by araima2001 | 28th Jan, 2017, 08:55: PM

Expert Answer:

begin mathsize 16px style Given space that comma
left parenthesis cot to the power of negative 1 end exponent straight x right parenthesis squared minus 3 left parenthesis cot to the power of negative 1 end exponent straight x right parenthesis plus 2 space greater than space 0
Let space cot to the power of negative 1 end exponent straight x space space equals space straight t
rightwards double arrow straight t squared space minus space 3 straight t space plus space 2 space greater than space 0
rightwards double arrow space left parenthesis straight t space minus space 2 right parenthesis left parenthesis straight t space minus space 1 right parenthesis space greater than thin space 0
For space left parenthesis straight t space minus space 2 right parenthesis left parenthesis straight t space minus space 1 right parenthesis space greater than thin space 0
either space straight t space minus space 2 space greater than 0 space space and space thin space straight t minus 1 space greater than thin space 0 space space space OR space space space space straight t space minus space 2 space less than 0 space space and space thin space straight t minus 1 space less than thin space 0

Case space 1 colon
straight t space minus space 2 space greater than 0 space space and space thin space straight t minus 1 space greater than thin space 0
rightwards double arrow space straight t space greater than thin space 2 space space space and space space straight t space greater than thin space 1
rightwards double arrow cot to the power of negative 1 end exponent straight x space greater than space 2 space space space and space space cot to the power of negative 1 end exponent straight x space greater than 1
rightwards double arrow straight x space greater than space cot space 2 space space and space straight x space greater than thin space cot space 1
So comma space straight x space greater than thin space cot space 1 space... left parenthesis Since space cot space 2 space less than space cot space 1 right parenthesis
Case space 2 colon
straight t space minus space 2 space less than 0 space space and space thin space straight t minus 1 space less than thin space 0
rightwards double arrow space straight t space less than thin space 2 space space space and space space straight t space less than thin space 1
rightwards double arrow cot to the power of negative 1 end exponent straight x space less than space 2 space space space and space space cot to the power of negative 1 end exponent straight x space less than 1
rightwards double arrow straight x space less than space cot space 2 space space and space straight x space less than thin space cot space 1
So comma space straight x space less than space cot space 2 space.... left parenthesis Since space cot space 2 space less than space cot space 1 right parenthesis

So comma space from space case space 1 space and space case space 2 comma space
straight x space less than space cot space 2 space or space straight x space greater than thin space cot space 1
end style

Answered by Rebecca Fernandes | 29th Jan, 2017, 08:15: PM

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