then which of the following statements is are correct 1 There are two values of q satisfying the ab...........

Quantitative Aptitude (CDS) Trignometry

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$If\: \frac{cos^{2}\theta -3cos\theta+2}{sin^{2}\theta}=1,where\: 0<\theta<\frac{\pi }{2},$

then which of the following statements is/are correct?

1. There are two values of q satisfying the above equation.

2. $\theta$ = 60° is satisfied by the above equation.

Select the correct answer using the code given below.

Only 1

Only 2

Both 1 and 2

Neither 1 nor 2

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Explanation:

=> cos² $\theta$ -3cos $\theta$ + 1 + 1 - sin² $\theta$ = 0
=> cos² $\theta$ -3cos $\theta$ +1+ cos² $\theta$ = 0
=> 2cos² $\theta$ -3cos $\theta$ +1= 0
=> (2cos $\theta$ -1)(cos $\theta$ - 1) = 0
=> cos $\theta$ = 1/2 or cos $\theta$ =1
=> $\theta$ =60^o or $\theta$ =0^{o

Hence both statements are correct.}