A.Verify the identity.

B.Determine if the identity is true for the given value of x. Explain.

[cot(x) – 1] / [cot(x) + 1] = [1 – tan(x)] / [1 + tan(x)], x = π/4

I solved A and I believe it's true; however, I need help with B.

Put in for x the value.

[cot(x) – 1] / [cot(x) + 1] = [1 – tan(x)] / [1 + tan(x)]
or
[cot(PI/4) – 1] / [cot(PI/4) + 1] = [1 – tan(PI/4)] / [1 + tan(PI/4)]

or
(1-1)/2=?=(1-1)/(1+1)
0=0

To determine if the identity is true for the given value of x, which is x = π/4, we need to substitute the value of x into both sides of the equation and simplify.

Let's start with the left side of the equation:

[cot(x) – 1] / [cot(x) + 1]

Substituting x = π/4:

[cot(π/4) – 1] / [cot(π/4) + 1]

Now, let's find the cotangent of π/4. The cotangent is the reciprocal of the tangent function.

cot(π/4) = 1 / tan(π/4)

We know that tan(π/4) = 1, so we can substitute this value:

cot(π/4) = 1 / 1 = 1

Now we can substitute this value back into the equation:

[(1) – 1] / [(1) + 1]

Simplifying further:

[0] / [2] = 0

So, the left side of the equation is 0 when x = π/4.

Now let's evaluate the right side of the equation:

[1 – tan(x)] / [1 + tan(x)]

Substituting x = π/4:

[1 – tan(π/4)] / [1 + tan(π/4)]

Since we already know tan(π/4) = 1:

[1 – 1] / [1 + 1]

[0] / [2] = 0

So, the right side of the equation is also 0 when x = π/4.

Since both the left side and the right side of the equation evaluate to 0 when x = π/4, we can conclude that the identity is true for this particular value of x.