Question

Solve sec (y + pi/2) = - 2 for 0 < y < pi radians.
Help needed!! anyone?

Answer 1

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