I am supposed to find angle $\phi$ by which the coordinate axes must be rotated so that the equation of the pair of straight lines $ax^2+2hxy+by^2=0$ becomes independent of $xy$ term in the rotated coordinate axes.
My Attempt
$$a(x\cos\phi+y\sin\phi)^2+2h(x\cos\phi+y\sin\phi)(y\cos\phi-x\sin\phi)+b(y\cos\phi-x\sin\phi)^2\\ xy \text{ term}\rightarrow (a-b)\sin(2\phi)+2h\cos(2\phi)=0$$
$$\phi=\dfrac{1}{2}\arctan\left(\dfrac{2h}{b-a}\right)$$
In my book the answer is given to be $1/2\arctan(2h/(a-b))$. My take on this is that since rotation can be both clockwise or anticlockwise, both the books' answer and the answer I arrived at are correct. Is that so?