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Question:

(cosec θ - cot θ)² = ?. 0° < θ < 90°

Explanation:

(cosec θ - cot θ)2

= ${\left(\frac{1}{\mathrm{sin\theta }}-\frac{\mathrm{cos\theta }}{\mathrm{sin\theta }}\right)}^2$

= ${\left(\frac{1-\cos \theta }{\mathrm{sin\theta }}\right)}^2$

= $\frac{{(1-\cos \theta )}^2}{{\sin }^2\theta }$

= $\frac{{(1-\cos \theta )}^2}{1-{\cos }^2\theta }$

= $\frac{(1-\cos \theta )(1-\cos \theta )}{(1-\cos \theta )(1+\cos \theta )}$

=$\frac{1-\cos \theta }{1+\cos \theta }$

Hence, option (b).