There are many ways to paint shadows. For covering large areas such as your example, here is one way.
Create a new layer above your texture layer and fill it with black (or dark gray). Change the layer blend mode to Multiply.
Add a layer mask to the black layer. Fill the layer mask entirely with Black.
Select a large, soft brush and set the Flow to about 5%. Paint with white in the layer mask to gradually reveal the dark shadows. With the Flow set at 5% you can better control how much shadow you reveal by painting multiple brush strokes over the shaded area.
You can also do the same thing with white to create highlights. Painting highlights next to shadows is a good way to simulate depth.
Fill a new layer with white and change the layer blend mode to Soft Light.
Add a layer mask and fill the mask with black.
Select a soft brush and set the Flow to 5% to gradually paint the highlights.
Another technique I suggest is using a curves adjustment layer to apply a natural looking shadow. Black is usually not the best for shadowing. A curves adjustment layer allows you to darken (or lighten) the existing tonal or luminosity values of the subject/image naturally.
Open the image.
Go to > LAYER > NEW ADJUSTMENT LAYER > CURVES.
Adjust the Curves Adjustment Layer (CAL) to darken the image.
Click on the CAL's layer mask and hit Cmd/Cntrl + I to invert. The layer mask should now be black.
Select the Brush Tool and use a soft brush with the FLOW set to 2% to 5%. Paint on the canvas with white as your foreground color.
Darkened naturally with the CAL:
After the CAL's layer mask has been inverted and the shadows have been painted in:
I use often the following technique (I am not a pro). I create a PNG file for the shadows. In the following example there are two lighting sources. Therefore, two shadows, one lighter and smoother as the second.
When done, you can use it as a layer to set under the subject. Then you apply an "Overlay" blending mode and can choose between warm or cold shadows and smooth or hard shadows.