Question

Solve: $\frac{co{s}^2\theta -3cos\theta +2}{si{n}^2\theta }=2$ [4 MARKS]

Answer 1

Formula: 2 Marks
Proof: 2 Marks

$\begin{array}{cc}Given& \frac{co{s}^2\theta -3cos\theta +2}{si{n}^2\theta }=2\\ \Rightarrow & co{s}^2\theta -3cos\theta +2=2si{n}^2\theta \\ \Rightarrow & c{s}^2\theta -3cos{\theta }_{+}2=2(1-co{s}^2\theta )\\ \Rightarrow & co{s}^2\theta -3cos\theta +2-2+2co{s}^2\theta =0\\ \Rightarrow & 3co{s}^2\theta -3cos\theta =0\Rightarrow 3cos\theta (cos\theta -1)=0\\ \Rightarrow & Either3cos\theta =0orcos\theta -1=0\\ \Rightarrow & cos\theta =0orcos\theta =1\\ \Rightarrow & cos\theta =cos{90}^{\circ }orcos\theta =cos{0}^{\circ }\\ \Rightarrow & \theta ={90}^{\circ }or\theta =0^{\circ }\end{array}$