If x= _e [ ( 4 + ) ] and ( - 4 , 4 ) , then consider the following statements I. x= 2 II. x=- 2

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Correct answer: C. Both I and II are true

aligned & We have, x= [ ( 4 + ) ] & x= e^x+e^ -x 2 & = e^ [ ( 4 + ) ] +e^ - [ ( 4 + ) ] 2 & = ( 4 + )+ 1 ( 4 + ) 2 & = ^2 ( 4 + )+1 2 ( 4 + ) = cosec ^2 ( 4 + ) 2 ( 4 + ) & = 1 2 ^2 ( 4 + ) ( 4 + ) ( 4 + ) & = 1 2 ( 4 + ) ( 4 + ) & = 1 (2 ( 4 + ) ) = 1 ( 2 +2 ) = 1 2 = 2 & aligned Hence, statement I is true. Again, x= e^x-e^ -x 2 aligned & = e^ ( ( 4 + ) ) -e^ - ( ( 4 + ) ) 2 & = ( 4 + )- 1 ( 4 + ) 2 & = ^2 ( 4 + )-1 2 ( 4 + ) = 1- ^2 ( 4 + ) 2 ( 4 + ) & = 1 ( ( 4 + ) 1- ^2 ( 4 + ) ) (2 ( 4 + ) ) 1 & = 1 ( 2 +2 ) 1

If x= _e [ ( 4 + ) ] and ( - 4 , 4 ) , then consider the following statements I. x= 2 II. x=- 2

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