How many values are there for the cot(3x-pi/4)!=-1cot(3xπ4)1? [-5,5][5,5]

1 Answer
Apr 22, 2018

There are infinitely many values of x that will make the cotangent function not equal to -1 within the domain [-5,5][5,5].

Explanation:

Given: cot(3x-pi/4)!=-1, {x in RR|-5 <= x <=5}

Use the identity cot(u) = 1/tan(u) where u = 3x-pi/4:

1/tan(3x-pi/4)!=-1, {x in RR|-5 <= x <=5}

tan(3x-pi/4)!=1/-1, {x in RR|-5 <= x <=5}

tan(3x-pi/4)!=-1, {x in RR|-5 <= x <=5}

3x-pi/4!=tan^-1(-1), {x in RR|-5 <= x <=5}

3x-pi/4!=(3pi)/4+npi, {x in RR|-5 <= x <=5}, n in ZZ

3x != pi+npi, {x in RR|-5 <= x <=5}, n in ZZ

x != pi/3+npi/3, {x in RR|-5 <= x <=5}, n in ZZ

There are infinitely many values of x that make the above inequality true within the domain restrictions.