Question

prove
\frac{ \sin( \alpha ) }{1 - \cos( \alpha ) } =cosec(α)+cot(α)[/tex]
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Answer 1

Answer:

Step-by-step explanation:

$\frac{sin\alpha}{1-cos\alpha}\\=\frac{sin\alpha}{1-cos\alpha} \times \frac{1+cos\alpha}{1+cos\alpha}\\=\frac{sin\alpha+(sin\alpha \times cos\alpha)}{1- cos^2\alpha}\\=\frac{sin\alpha+(sin\alpha \times cos\alpha)}{sin^2\alpha}\\\\=\frac{sin\alpha}{sin^2\alpha} + \frac{sin\alpha \times cos\alpha}{sin^2\alpha}\\=\frac{1}{sin\alpha} + \frac{cos\alpha}{sin\alpha}\\=cosec\alpha + cot\alpha$