To find the value of the expression
tan−1()−tan−1(), we can use the properties of the inverse tangent (or arctangent) function. Specifically, we will use the formula related to the difference of two arctangents:
tan−1(x)−tan−1(y)=tan−1()For our problem, let's set
x= and
y=. Substituting these values into the formula above, we get:
tan−1()−tan−1()=tan−1()To simplify this expression, we need to find a common denominator for the numerator and simplify the denominator as follows:
The numerator:
−Finding a common denominator:
==The denominator:
1+⋅Simplifying the product:
1+=1+==Thus, we have:
tan−1()=tan−1(1)We know that:
tan−1(1)=So:
tan−1()−tan−1()=