Question : Which of the following is a value of $\theta$, when $\cos ^2 \theta-2+\cos \theta=0$?
Option 1: 60°
Option 2: 90°
Option 3: 30°
Option 4: 0°
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Correct Answer: 0°
Solution :
Given, $\cos ^2 \theta-2+\cos \theta=0$
⇒ $\cos ^2 \theta+2\cos \theta-\cos\theta-2=0$
⇒ $\cos \theta(\cos \theta+2)-1(\cos \theta+2)=0$
⇒ $(\cos \theta+2)(cos \theta-1)=0$
⇒ $\cos \theta=-2$ or $\cos \theta=1$
Since the range of $\cos\theta$ is –1 < $\cos \theta$ < 1
Hence, $\cos\theta$ cannot be –2.
So, $\cos \theta=1⇒\theta= 0°$
Hence, the correct answer is 0°.
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