Chapter EP, Problem 14.5.8EP

To determine

To find: the solution of the equation all value of $\text{θ}$ if $\text{θ}$ is measured in radian.

Answer to Problem 14.5.8EP

$\text{θ=nπ-}\frac{\text{π}}{\text{2}}$ , $\text{n}\in \text{Z}$ , $\text{θ=2nπ+}\frac{\text{π}}{6}$ , $\text{n}\in \text{Z}$ and $\text{θ=2nπ+}\frac{\text{5π}}{6}$ .

Explanation of Solution

Given:

  $\text{cosθ-2cosθsinθ=0}$ .

Concept used:

According to the trigonometric formula:

  $\text{2cosθsinθ=sin2θ}$ .

Calculation:

  $\text{cosθ-2cosθsinθ=0}$ .

According to the trigonometric formula:

  $\text{2cosθsinθ=sin2θ}$ .

  $\Rightarrow \text{cosθ-sin2θ=0}$ .

  $\Rightarrow \text{cosθ=sin2θ}$ .

Or

  $\text{cosθ}\left(\text{1-2sinθ}\right)\text{=0}$ .

$\text{cosθ=0}$ and $\text{1-2sinθ=0}\Rightarrow \text{sinθ=}\frac{\text{1}}{\text{2}}$ .

Hence, $\text{θ=nπ-}\frac{\text{π}}{\text{2}}$ , $\text{n}\in \text{Z}$ , $\text{θ=2nπ+}\frac{\text{π}}{6}$ , $\text{n}\in \text{Z}$ and $\text{θ=2nπ+}\frac{\text{5π}}{6}$ .