how does
secx(tanx + tan^2x- sec^2x)
simplified to
sec x (tanx -1)?
you should have come across the identity
sec^2x = tan^2x + 1
(by dividing each term of sin^2 + cos^2x = 1 by cos^2x )
sub back in , and you got it
To simplify the expression sec(x)(tan(x) + tan^2(x) - sec^2(x)), we can start by using trigonometric identities and properties to rewrite the terms in the expression.
First, let's rewrite tan^2(x) as sec^2(x) - 1. This result comes from the Pythagorean Identity, which states that sec^2(x) = 1 + tan^2(x).
Using this, we can then rewrite the expression as sec(x)(tan(x) + sec^2(x) - 1 - sec^2(x)).
Notice that the sec^2(x) terms cancel out, leaving us with sec(x)(tan(x) - 1).
Therefore, sec(x)(tan(x) + tan^2(x) - sec^2(x)) simplifies to sec(x)(tan(x) - 1).