If 12cot2θ-31cosecθ+32=0, the the value of sinθ is
35or1
23or-23
45or34
±12
Explanation for correct option:
Step-1: Simplify the given data.
Given, 12cot2θ-31cosecθ+32=0,
⇒ 12cos2θsin2θ-311sinθ+32=0
⇒ 12cos2θ-31sinθ+32sin2θ=0
⇒12cos2θ+12sin2θ-31sinθ+20sin2θ=0∵cos2θ+sin2θ=1
⇒ 20sin2θ-31sinθ+12=0
Step-2: Solve the quadratic equation -b±b2-4ac2a.
⇒sinθ=--31±312-4×20×122×20
⇒sinθ=31±961-9602×20
⇒sinθ=3240or3040
⇒sinθ=45or34
Hence, correct answer is option C