Verify only working with one side:

cos^2x + tan^2x cos^2x = 1

tan^x*cos^2x can be replaced with sin^2x, since tan^2x = sin^2x/cos^2x

cos^2 + sin^2x = 1

q.e.d.

Thank you.!

To verify the equation cos^2x + tan^2x cos^2x = 1, we can simplify both sides of the equation and check if they are equal.

First, let's simplify the left side of the equation:

cos^2x + tan^2x cos^2x

Using the identity tan^2x = sin^2x/cos^2x:

cos^2x + (sin^2x/cos^2x) * cos^2x

Simplifying further:

cos^2x + sin^2x

Now, we can use the Pythagorean identity sin^2x + cos^2x = 1:

cos^2x + sin^2x = 1

Since the simplified left side of the equation is equal to 1, and the right side of the equation is also 1, we can conclude that the equation cos^2x + tan^2x cos^2x = 1 is verified.