  We present cosmological parameter constraints from a joint analysis of three
cosmological probes: the tomographic cosmic shear signal in $\sim$450 deg$^2$
of data from the Kilo Degree Survey (KiDS), the galaxy-matter cross-correlation
signal of galaxies from the Galaxies And Mass Assembly (GAMA) survey determined
with KiDS weak lensing, and the angular correlation function of the same GAMA
galaxies. We use fast power spectrum estimators that are based on simple
integrals over the real-space correlation functions, and show that they are
practically unbiased over relevant angular frequency ranges. We test our full
pipeline on numerical simulations that are tailored to KiDS and retrieve the
input cosmology. By fitting different combinations of power spectra, we
demonstrate that the three probes are internally consistent. For all probes
combined, we obtain $S_8\equiv \sigma_8 \sqrt{\Omega_{\rm
m}/0.3}=0.800_{-0.027}^{+0.029}$, consistent with Planck and the fiducial
KiDS-450 cosmic shear correlation function results. Marginalising over wide
priors on the mean of the tomographic redshift distributions yields consistent
results for $S_8$ with an increase of $28\%$ in the error. The combination of
probes results in a $26\%$ reduction in uncertainties of $S_8$ over using the
cosmic shear power spectra alone. The main gain from these additional probes
comes through their constraining power on nuisance parameters, such as the
galaxy intrinsic alignment amplitude or potential shifts in the redshift
distributions, which are up to a factor of two better constrained compared to
using cosmic shear alone, demonstrating the value of large-scale structure
probe combination.
