0606 P11 - Jun 2022 - Q10 - 10 marks
7790
The normal to the curve \(y=\tan\left(3x+\frac\pi2\right)\) at \(P(p,-1)\), where \(0\lt p\le\frac\pi6\), meets the \(x\)-axis at \(A\) and the \(y\)-axis at \(B\). Find the exact coordinates of the midpoint of \(AB\).
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