A) \[\frac{3}{5}\] or 1
B) \[-\sin (B+2C)=\frac{1}{2}\] or \[\frac{-2}{3}\]
C) \[\frac{4}{5}\] or \[\frac{3}{4}\]
D) \[\pm \frac{1}{2}\]
Correct Answer: C
Solution :
\[12{{\cot }^{2}}\theta -31\cos ec\theta +32=0\] \[12(\text{cos}\text{e}{{\text{c}}^{2}}\theta -1)-31\text{cos}\text{ec }\theta +\text{32}=\text{0}\] \[12\text{cos}\text{e}{{\text{c}}^{2}}\theta -31\,\text{cos}\text{ec }\theta +\text{20}=\text{0}\] \[12\,\text{cos}\text{e}{{\text{c}}^{2}}\theta -16\,\,\text{cos}\text{ec }\theta -15\text{cos}\text{ec}\theta +20=\text{0}\] \[(4\cos \text{ec}\theta -5)(3\cos \text{ec}\theta -4)=0\] \[\text{cos}\text{ec}\theta =\frac{5}{4},\frac{4}{3}\]; \ \[\sin \theta =\frac{4}{5},\frac{3}{4}\].
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