Drawing a pair of lines to the x-axis and y-axis from a point along a curve

I have some plot like the following:

Plot[Cos[x], {x, -10, 10}, AxesLabel -> {Style["x-axis", 12], Style["y-axis", 12]}, ImageSize -> {650, 650}]

I'd like to be able to specify a point along the x-axis and draw a line of some color from this point to a point immediately above or below it falling along the given curve, and then draw a line from this point on the curve to a point immediately to the left or right of the point on the curve to a point on the y-axis (wherever either of these two axes are positioned). Is there a built-in way to do this in Mathematica 9?

The purpose of this is to make it obvious where a point p on the curve falls along the x-axis and y-axis in the plot.

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Like this, Epilog?

With[{expr = Cos[x], x0 = 5.4},
Plot[expr, {x, -10, 10},
AxesLabel -> {Style["x-axis", 12], Style["y-axis", 12]},
ImageSize -> {650, 650},
Epilog -> {Lighter@Red,
Line[{{x0, 0}, {x0, expr /. x -> x0}, {0, expr /. x -> x0}}]}]
] Or perhaps with GridLines?

With[{expr = Cos[x], x0 = 5.4},
Plot[expr, {x, -10, 10},
AxesLabel -> {Style["x-axis", 12], Style["y-axis", 12]},
ImageSize -> {650, 650},
GridLines -> {{x0}, {expr /. x -> x0}},
GridLinesStyle -> Lighter@Red]
] 