Chapter 13.5, Problem 58PPS

To determine

To shown : Error in either of shown calculation and explain, is either of them is correct.

Answer to Problem 58PPS

Both are wrong.

Explanation of Solution

Given information :

We know that, Trigonometric equation $\text{2 sin }\theta \text{ cos }\theta \text{ = sin }\theta \text{ for 0°}\le \theta \le \text{360°}\text{.}$

Jennifer and tat solved given equation.

Calculation :

The given equation is

  $\begin{array}{l}\text{2}\sin \theta \cos \theta =\sin \theta \\ \Rightarrow 2\sin \theta \cdot \cos \theta -\sin \theta =0\\ \Rightarrow \sin \theta (2\cos \theta -1)=0\\ \Rightarrow \sin \theta =0\text{and}2\cos \theta -1=0\\ \Rightarrow \cos \theta =\frac{1}{2}\\ \theta =0,180°,360°\text{and}\theta =60°,300°\end{array}$

Solutions are $\text{0}°,60°,300°,360°,180°.$

Both have solved wrong.

Jennifer divided both sides by $\text{sin }\theta$ , division should be done and cancelled from numerator. Since it will vanishes values of $\text{sin }\theta =0$ .

Tat solved equation wrong, he should not write.

  $-\sin \theta =-\sin \theta \text{and}2\cos \theta =0$

For gives trigonometric equation. He lost values $\text{sin }\theta \text{ = 0 and cos }\theta \text{ = }\frac{\text{1}}{\text{2}}$ .