Question

Write the value of $\cos {\mathrm{ec}}^2\theta \left(1+\cos \theta \right)\left(1-\cos \theta \right)$.

Answer 1

$$\begin{gathered} \cos {\mathrm{ec}}^2\theta \left(1+\cos \theta \right)\left(1-\cos \theta \right) \\ ={\mathrm{cosec}}^2\theta \left(1-{\cos }^2\theta \right) \\ =\frac{1}{{\sin }^2\theta }\times {\sin }^2\theta \\ =1 \end{gathered}$$

Disclaimer: The question given in the textbook is incorrect. There should be $\cos \theta$ instead $\sin \theta$. The solution provided here is of the same.