Question

How do you prove `sec^2 theta - cos^2 theta sec^2 theta`?

Answer 1

See explanation to see if I answered your question. I proved that `sec^2 theta - cos^2 theta sec^2 theta` equals `tan^2 theta`. Please let me know if I answered your question.

Explanation:

I'm not sure what to prove here, but I think I have an idea.

`sec^2 theta - cos^2 theta sec^2 theta`

`sec theta` always equals `1/cos theta` (Reciprocal Identity)

`sec^2 theta - (cos^2 theta/1 * 1/cos^2 theta)`

`sec^2 theta - (cancel(cos^2 theta)/1 * 1/cancel(cos^2 theta))`

`sec^2 theta - (1)`

`1 + tan^2 theta` always equals `sec^2 theta`, or `1 + tan^2 theta = sec^2 theta` (Pythagorean Identity)

`sec^2 theta -1`

`tan^2 theta`