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Given the function f(x)=sin2ωx2+12sinωx−12 (ω>0)f(x)=\sin^2 \dfrac{\omega x}{2}+\dfrac{1}{2} \sin \omega x - \dfrac{1}{2}\ (\omega>0)f(x)=sin22ωx+21sinωx−21 (ω>0), x∈Rx \in \mathbb Rx∈R.
If f(x)=0f(x)=0f(x)=0 has no roots for x∈(π,2π)x \in (\pi, 2\pi)x∈(π,2π), then find the range of ω\omegaω.
A. (0,18]A.\ (0,\dfrac{1}{8}]A. (0,81]
B. (0,14]∪[58,1]B.\ (0,\dfrac{1}{4}] \cup [\dfrac{5}{8},1]B. (0,41]∪[85,1]
C. (0,58]C.\ (0,\dfrac{5}{8}]C. (0,85]
D. (0,18]∪[14,58]D.\ (0,\dfrac{1}{8}] \cup [\dfrac{1}{4},\dfrac{5}{8}]D. (0,81]∪[41,85]
Have a look at my problem set: SAT 1000 problems
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