If 12 cot^2 theta - 31 csc theta + 32 = 0,the | vedclass

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(C) Given the equation: $12 \cot^2 	heta - 31 \csc 	heta + 32 = 0$Using the identity $\cot^2 	heta = \csc^2 	heta - 1$,we substitute:$12(\csc^2

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$\frac{4}{5}$ or $\frac{3}{4}$

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(C) Given the equation: $12 \cot^2 	heta - 31 \csc 	heta + 32 = 0$Using the identity $\cot^2 	heta = \csc^2 	heta - 1$,we substitute:$12(\csc^2 	heta - 1) - 31 \csc 	heta + 32 = 0$Simplify the equation:$12 \csc^2 	heta - 12 - 31 \csc 	heta + 32 = 0$$12 \csc^2 	heta - 31 \csc 	heta + 20 = 0$Factor the quadratic equation in terms of $\csc 	heta$:$12 \csc^2 	heta - 16 \csc 	heta - 15 \csc 	heta + 20 = 0$$4 \csc 	heta (3 \csc 	heta - 4) - 5 (3 \csc 	heta - 4) = 0$$(4 \csc 	heta - 5)(3 \csc 	heta - 4) = 0$This gives two possible values for $\csc 	heta$:$\csc 	heta = \frac{5}{4}$ or $\csc 	heta = \frac{4}{3}$Since $\sin 	heta = \frac{1}{\csc 	heta}$,we have:$\sin 	heta = \frac{4}{5}$ or $\sin 	heta = \frac{3}{4}$.

If $12 \cot^2 \theta - 31 \csc \theta + 32 = 0$,then the value of $\sin \theta$ is

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