Question

Prove the identity with rules (1-cos(-x)) / (sec(-x)-1) =cosx

Answer 1

By using the rules:

$cos(-x) = cos(x)\\\\sec(x) = \frac{1}{cos(x)}$

We have proven the identity. Below you can follow the demonstration.

How to prove the identity?

Here you need to remember two things:

$cos(-x) = cos(x)\\\\sec(x) = \frac{1}{cos(x)}$

Here we have the expression:

$\frac{1 - cos(-x)}{sec(-x) - 1}$

By using the first rule, we can rewrite:

$\frac{1 - cos(-x)}{sec(-x) - 1} = \frac{1 - cos(x)}{sec(x) - 1}$

By using the second rule, we can rewrite:

$\frac{1 - cos(x)}{sec(x) - 1} = \frac{1 - cos(x)}{\frac{1}{cos(x)} - 1}$

Now if we multiply and divide by cos(x), we get:

$\frac{1 - cos(x)}{\frac{1}{cos(x)} - 1} = \frac{1 - cos(x)}{\frac{1}{cos(x)} - 1} *\frac{cos(x)}{cos(x) } = \frac{(1- cos(x))*cos(x)}{1 - cos(x)} = cos(x)$

In this way, the identity was proven.

If you want to learn more about trigonometric identities:

brainly.com/question/7331447

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