Math Problem Statement
prove that 2(1+cos8theta)=(x^4-4x^2+2)^2 where x=2costheta
Solution
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Multiple Angle Formulas
Algebraic Expansion
Chebyshev Polynomials
Formulas
cos(2θ) = 2cos²(θ) - 1
cos(4θ) = 2cos²(2θ) - 1
cos(8θ) = 2cos²(4θ) - 1
x = 2cos(θ)
Theorems
Cosine Multiple Angle Identity
Trigonometric Polynomial Expansion
Suitable Grade Level
Grades 11-12 (Advanced Trigonometry)
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