Question

Find your own values that prove that tan(u-v) does not equal tan u - tan v. Show your work and explain why you chose these values.

Answer 1

To prove that tan(u - v) does not equal tan u - tan v, we start by assuming values for u and v.

To do this, we assume the following values

$\mathbf{u = 75}$

$\mathbf{v = 45}$

So, we have:

$\mathbf{tan(u - v) \ne tan(u) - tan(v)}$

Substitute the assumed values for u and v

$\mathbf{tan(75 - 45) \ne tan(75) - tan(45)}$

Subtract 45 from 75

$\mathbf{tan(30) \ne tan(75) - tan(45)}$

Using a calculator, calculate the values of tan(30), tan(45) and tan(75)

So, we have:

$\mathbf{0.5774 \ne 3.7321 - 1}$

Subtract 1 from 3.7321

$\mathbf{0.5774 \ne 2.7321}$

Notice that the expression on the left-hand side and the expression on the right-hand side are not equal.

Hence, $\mathbf{tan(u - v) \ne tan(u) - tan(v)}$ is true

Read more about proofs of trigonometry at:

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