HW8sol - MAC1114 - Homework 8 Due Tuesday - March 15 • 1....

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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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