Mathematics

Mathematics

Problem

Let θ\theta be any acute angle. a. (i) Show that sin⁡4θ+cos⁡4θ=1−2sin⁡2θcos⁡2θ\sin^{4}\theta + \cos^{4}\theta = 1 - 2\sin^{2}\theta\cos^{2}\theta. b. (ii) If sin⁡θcos⁡θ=34\sin\theta\cos\theta=\dfrac{\sqrt{3}}{4}, find the value of sin⁡4θ+cos⁡4θ\sin^{4}\theta + \cos^{4}\theta. (Leave your answer in simplest radical form.)

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