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

User Flying Swissman
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1 Answer

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~~~~\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

User Asiyah
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