A robotic arm rotates such that its displacement angle α\alphaα in radians satisfies the drive torque equation: 3sinα(4cot22α−5)=8secα3 \sin \alpha (4 \cot^2 2\alpha - 5) = 8 \sec \alpha3sinα(4cot22α−5)=8secα
Show that this equation can be expressed in the form 12csc22α−16csc2α−27=012 \csc^2 2\alpha - 16 \csc 2\alpha - 27 = 012csc22α−16csc2α−27=0
Hence, for 0<α<π20 < \alpha < \frac{\pi}{2}0<α<2π, determine the possible values of the displacement angle α\alphaα, giving your answers to 3 significant figures.
