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
+1262 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
+23252 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.]
