Let ( ) be an acute angle of a right triangle.

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

Problem

Let θ\theta be an acute angle of a right triangle. (i) Using the definitions of the primary trigonometric ratios, prove that sin⁡θcos⁡θ=tan⁡θ\dfrac{\sin \theta}{\cos \theta} = \tan \theta. (ii) Hence or otherwise, simplify the expression sin⁡θ1−cos⁡θ+sin⁡θ1+cos⁡θ\dfrac{\sin \theta}{1-\cos \theta} + \dfrac{\sin \theta}{1+\cos \theta} and express your result entirely in terms of tan⁡θ\tan \theta.

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