Mathematics | VITEEE 2018 | Discussion Page

If $12 \cot^{2}\theta - 31Cosec \theta + 32 = 0$ , then the value of Sinθ is

A) 3/5 or 1

B) 2/3 or -2/3

C) 4/5 or 3/4

D) ± 1/2

Option C

$12 \cot^{2}\theta - 31Cosec \theta + 32 = 0$

$\Rightarrow 12\left(cosec^{2}\theta-1\right)- 31Cosec \theta+32=0$

$\Rightarrow 12 cosec^{2}\theta- 31Cosec \theta+20=0$

$\Rightarrow 12 cosec^{2}\theta- 16Cosec \theta - 15 cosec\theta+20=0$

$(4 cosec\theta - 5)(3 cosec\theta-4)= 0$

$Cosec\theta = 5/4,4/3 \therefore \sin\theta = 4/5,3/4$

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