For an acute angle

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

For an acute angle θ\theta, it is given that cos⁡θ=725\cos\theta = \dfrac{7}{25}. (i) Determine sin⁡θ\sin\theta. (ii) Evaluate sin⁡2θ−cos⁡2θ\sin^{2}\theta - \cos^{2}\theta. (iii) Using the values obtained, verify the relationship between sin⁡2θ\sin^{2}\theta and cos⁡2θ\cos^{2}\theta. (Show all steps.)

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