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.
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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.