sec^2x
To prove this identity, we need to start with the left-hand side of the equation and simplify it until we get the right-hand side. Here’s how:
Start with: 1 + tan^2x
Recall that tan^2x + 1 = sec^2x (this is another trig identity that you may have learned). So we can rewrite the left-hand side like this:
1 + tan^2x = 1 + tan^2x + 1 – 1
= tan^2x + 1 + 1 – 1
= tan^2x + 1
= sec^2x
Therefore, we have proved that 1 + tan^2x = sec^2x.
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