To simplify the expression 1 tan2x 1 tan2x, we need to clarify it first. It looks like there may be a small formatting issue. It seems you’re asking about the simplification of 1 + tan²(x).
Using the Pythagorean identity from trigonometry, we know that 1 + tan²(x) = sec²(x). This identity arises because:
- tan(x) is defined as sin(x)/cos(x),
- and therefore tan²(x) is (sin²(x)/cos²(x)).
From the Pythagorean identity, we have that sin²(x) + cos²(x) = 1. Rearranging gives us sin²(x) = 1 – cos²(x). Dividing the entire equation by cos²(x) yields:
sin²(x)/cos²(x) + 1 = 1/cos²(x)
This shows that 1 + tan²(x) = sec²(x).
So, to summarize, the simplification of 1 + tan²(x) results in sec²(x).