find solution of sec^-1(3x-2)=1.. work shown need help!

[djdavis2k]

Find the solution of the following equation, if the solution exists.

sec^-1(3x-2)=1

work shown:

since, sec x= 1/cos(x)

and since cos^-1(x)*cos(x)= x

therefore,

1/cos(3x-2)= 1

1/(cos^-1)(cos(3x-2))=1/cos^-1(1)

1/(3x-2)= 1/cos^-1(1)

1/(3x-2)= 1/0

therefore i got does not exist.. but I believe i made an error in the identities i used.. please help

 

[Deleted member 4993]

Find the solution of the following equation, if the solution exists.

sec^-1(3x-2)=1

work shown:

since, sec x= 1/cos(x)

and since cos^-1(x)*cos(x)= x

therefore,

1/cos(3x-2)= 1

1/(cos^-1)(cos(3x-2))=1/cos^-1(1)

1/(3x-2)= 1/cos^-1(1)

1/(3x-2)= 1/0

therefore i got does not exist.. but I believe i made an error in the identities i used.. please help

\(\displaystyle \sec^{-1}(3x-2) \, = \, 1\)

means

\(\displaystyle \sec(1) \, = \, 3x \, - \, 2\)

then

\(\displaystyle \cos(1) \, = \, \frac{1}{3x \, - \, 2}\)

Now continue.....