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Unformatted text preview: MAC1114  Homework 8
Due Tuesday  March 15 •
1. Verify each of the following identities: (1 + sin x)(1 − sin x) = cos2 x (note the typo in the original problem) (1 + sin x)(1 − sin x) = 1 − sin2 x = cos2 x
2. csc4 α − 2 csc2 α + 1 = cot4 α
csc4 α − 2 csc2 α + 1 = (csc2 α − 1)2 = (cot2 α)2 = cot4 α 3. cos2 t − sin2 t = 2 cos2 t − 1
cos2 t − sin2 t = cos2 t − (1 − cos2 t) = 2 cos2 t − 1 4. cos θ cot θ
− 1 = csc θ
1 − sin θ
Work on both sides for this one: cos θ cot θ
− 1 = csc θ
1 − sin θ
cos θ cot θ
= 1 + csc θ
1 − sin θ
cos θ cot θ = (1 + csc θ)(1 − sin θ) cos θ cot θ = 1 + csc θ − sin θ − csc θ sin θ
cos θ cot θ = csc θ − sin θ
cos θ cos θ
1 − sin2 θ
=
sin θ
sin θ cos2 θ
cos2 θ
=
sin θ
sin θ 1 ...
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 Spring '11
 Gentimis
 Algebra

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