Determining the define range?

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I need to determine the defined range for ${1+tanθ \over 1 + cotθ}$ = ${1-tanθ \over cotθ-1}$ , how should I do so?

The answer is θ (cannot equal to) kπ/4, k E Z

Guest Jun 11, 2020

jimkey17 · Answer 1 · 2020-06-11T08:32:42

actually any value of $θ$ is true if $θ$ is a variable but the equation ${1+\tanθ \over 1 + \cotθ}$ = ${1-\tanθ \over \cotθ-1}$ is an identity

geno3141 · Answer 2 · 2020-06-11T08:39:26

You need to eliminate all the possibilities for a denominator to be zero.

Since there is a tan(x) term, (and since tan(x) = sin(x)/cos(x) ), you must eliminate all the values that

make cos(x) = 0.

Since there is a cot(x) term, (and since cot(x) = cos(x)/sin(x) ), you must eliminate all the values that

make sin(x) = 0.

Since there is a denominator of 1 + cot(x), you must eliminate all the values that make cot(x) = -1.

Since there is a denominator of cot(x) - 1, you must eliminate all the values that make cot(x) = 1.

[And, remember that both tan(x) and cot(x) have a period of pi.]