GTA3 3.2 Homework Review Notes

42. a^2 - b^2


(1 - sin^2 ?)(1 + sin^2 ?)

option a -looking at the factor as a difference squares
1^2 - (sin ^2 ?)^2

1 - sin ^4 ?

option b -using fundamental identity
cos^2 ?(1+sin^2 ?)

cos^2 ? + cos^2 ? sin^2 ?

option c -looking at the first binomial as a difference of squares

1^2 - Sin^2 ?

(1 - sin ?)(1 + sin ?)(1 + sin^2 ?)

let's try starting with the more complicated side!

2 cos^2 ? - cos ^4 ? factor out a cos ^2 ?
cos^2 ? (2- cos^2 ?) use fundamenal identity

1 - sin ^2 ? (2 - (1 - sin^2 ?)) oh oh, now we are rollin! distibute the minus in the second parenthesis
(1 - sin2 ?)( 2-1+sin^2 ?)
(1 - sin2 ?)(1+sin^2 ?)