basic trig

• October 5th 2008, 02:31 PM
ss103
basic trig
Factor the expression and use the fundamental identities to simplify the two problems before.

1) 1-2 sin^2 x + sin^4 x

2) sec^3 x - sec^2 x - sec x + 1

Thank you!
• October 5th 2008, 02:39 PM
icemanfan
1. $1 - 2 \sin^2 x + \sin^4 x$

Substitute $u = \sin^2 x$ to yield:

$1 - 2u + u^2 = (u - 1)^2 = (1 - u)^2$

Back substituting:

$(1 - u)^2 = (1 - \sin^2 x)^2 = (\cos^2 x)^2 = \cos^4 x$

2. $\sec^3 x - \sec^2 x - \sec x + 1$

Substitute $u = \sec x$ to yield:

$u^3 - u^2 - u + 1 = (u - 1)^2(u + 1)$

Back substituting:

$(u - 1)^2(u + 1) = (\sec x - 1)^2(\sec x + 1)$