A curve C C\,C is defined by the equation
x=3tan(y+π3)x∈R,−5π6<y<π6 x = 3\tan\left(y + \frac{\pi}{3}\right) \quad x \in \mathbb{R}, \quad -\frac{5\pi}{6} < y < \frac{\pi}{6} x=3tan(y+3π)x∈R,−65π<y<6πShow that
dydx=ax2+b \frac{dy}{dx} = \frac{a}{x^2 + b} dxdy=x2+bawhere a a\,a and b b\,b are integers to be determined.
The point P P\,P on C C\,C has yyy-coordinate −π12\displaystyle -\frac{\pi}{12}−12π. The tangent to C C\,C at P P\,P intersects the xxx-axis at the point QQQ. Determine the exact xxx-coordinate of QQQ.
