[tex]~~~~\sec\left(y+\dfrac{\pi}2 \right) = -2\\\\\\\implies \left[\cos \left( y+ \dfrac{\pi}2 \right) \right]^{-1} = -2\\\\\\\implies \left( \cos y \cos \dfrac{\pi}2 -\sin y \sin \dfrac{\pi}2 \right)^{-1} =-2\\\\\\\implies \left(0- \sin y \right)^{-1} =-2\\\\\\\implies \left(-\sin y \right)^{-1} = -2\\\\\\\implies \sin y = \dfrac 12\\\\\\\implies y = n\pi + (-1)^{n} \dfrac{\pi}6\\\\\text{In the interval, }~(0,\pi)\\\\\\y= \dfrac{\pi}6, ~\dfrac{5\pi}6[/tex]
