Mathematics

Mathematics

Problem

Let θ\theta be an acute angle such that sin⁡θ=35\sin\theta = \dfrac{3}{5}. (a) Calculate cos⁡θ\cos\theta. (b) Hence find tan⁡θ\tan\theta. (c) Evaluate (1+sin⁡θ)(1−sin⁡θ)(1+\sin\theta)(1-\sin\theta) and show that the result equals cos⁡2θ\cos^{2}\theta for this value of θ\theta.

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