Question

how do I prove (1-sin^4(theta))/(1+sin^2(theta)) =cos^2(theta)

Answer 1

factor the numerator on the left hand side
(think difference of squares)

Answer 2

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

Answer 3

right! and you see something cancels

Answer 4

then I cancel out and use which Identity

Answer 5

\[\frac{(1-\sin^2(x))\cancel{(1+\sin^2(x))}}{\cancel{1+\sin^2(x)}}\]
think Pythagorean identity

Answer 6

yes you are right I just could not figure it out but I forgot that any of the steps in the Pythagorean make it right
Thanks so much!

Answer 7

right the one you want is the one that says sin^2(x)+cos^2(x)=1

Answer 8

yes Thanks Freckles

Answer 9

np