Algebra and Trigonometry (Structure and Method Book 2, Texas

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Illustration 3: If cos (α – β) = 1 and cos (α + β) = 1/e, where α, β ∈ [-π, π], then the values of α and β satisfying both the equations is/are Solution: It is given in the question that cos (α – β) = 1 and cos (α + β) = 1/e, where α, β ∈ [-π, π]. α – β = 0, 2π, -2π Hence, α – β = 0 (since α, β ∈ [-π, π]) So, the number of solutions of above will be number of points of intersection of the curves y = cos 2α and y = 1/e, where α, β ∈ [-π, π] It is quite clear that there are four solutions corresponding to four points of intersection P1, P2, P3 and P4.

Pages: 0

Publisher: Houghton Mifflin Company (1990)

ISBN: 0395516412

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