Chapter 14.5, Problem 5BCYP

To determine

To calculate:The general solution from the given equation.

Answer to Problem 5BCYP

  $n\pi ,n\in zorm\pi +{(-1)}^m\frac{7\pi }{6},m\in z.$

Explanation of Solution

Given Information: An Equation $\frac{\cos \theta }{\cot \theta }+2{\sin }^2\theta =0$ is given.

Formula used: $\cot \theta =\frac{\cos \theta }{\sin \theta },\sin \theta =\sin \alpha \Rightarrow \theta =n\pi +{(-1)}^n\alpha ,\alpha \in z$

Calculation:

  $\begin{array}{l}GivenEquationcanbewrittenas\\ \frac{\cos \theta }{\cos \theta }\sin \theta +2{\sin }^2\theta =0\\ \therefore \sin \theta +2{\sin }^2\theta =0\\ \therefore \sin \theta (1+2\sin \theta )=0\\ \therefore \sin \theta =0or\sin \theta =\frac{-1}{2}\\ \therefore \theta =n\pi ,n\in zor\theta =m\pi +{(}^{-}\frac{7\pi }{6},m\in z.\end{array}$