Let be an acute angle such that

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Let θ\theta be an acute angle such that tan⁡θ=724\tan\theta = \dfrac{7}{24}. Work through the following tasks. (i) Calculate sin⁡θ\sin\theta and cos⁡θ\cos\theta. (ii) Find the numerical value of sin⁡θ+cos⁡θsin⁡θ−cos⁡θ\dfrac{\sin\theta + \cos\theta}{\sin\theta - \cos\theta}. (iii) Using the ratios obtained, compute the product sin⁡θcos⁡θ\sin\theta \cos\theta and express it as a simplified fraction.

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