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TrigonometrySuperchallengeTrigonometric Identities

Trigonometric Identities · Superchallenge problem

An angle θ\theta with 0<θ<π40<\theta<\dfrac{\pi}{4} satisfies sin⁡8θ+cos⁡8θ=1781\sin^8\theta+\cos^8\theta=\dfrac{17}{81}. Find cos⁡2θ−sin⁡2θ\cos^2\theta-\sin^2\theta.