If sec ndash cos 3 2 where is a positive acute triangle then the value of sec is...........

Quantitative Aptitude ( CCS) Trignometry

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If sec $\Theta$ –cos $\Theta$ = 3/2 where $\Theta$ is a positive acute triangle then the value of sec $\Theta$ is

-1/2

-2

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Explanation:

1/cos $\Theta$ –cos $\Theta$ = 3/2
2(1-cos² $\Theta$ )=3 cos $\Theta$
2 cos² $\Theta$ + 3 cos $\Theta$ -2=0
2 cos² $\Theta$ + 4 cos $\Theta$ –cos $\Theta$ -2 =0
2cos(cos $\Theta$ +2)-1(cos $\Theta$ + 2) =0
(cos $\Theta$ + 2) (2cos $\Theta$ -1) = 0
Cos $\Theta$ =1/2 , cos $\Theta$ -2
∴sec $\Theta$ =2