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Solve (tan 3x - tan 2x)/(1+tan 3x tan 2x...

Solve `(tan 3x - tan 2x)/(1+tan 3x tan 2x)=1`.

Text Solution

Verified by Experts

We have
`(tan 3x-tan 2x)/(1+tan 3x tan 2x)=1`
`rArr tan (3x-2x)=1`
or `tan x=1`
One of the principal solution of the equation is `x=pi/4`. Since period of `tan x` is `pi`, general solution is given by
`x=npi+pi/4, n in Z`.
But for these values of x, term `(tan 2x)` in original equation is not defined.
So, `x=n pi+pi/4, n in Z` is not the solution of the equation.
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