Is it ever possible that cos(a−b)=cos ⁡a − cos ⁡b?

yes

Step-by-step explanation:

I'm going to give you a slightly different answer, but it's going to make sense :-)

First, let's review what "sin" and "cos" really mean. They are functions that take as an input an angle, which we call theta. They output the base (cos) and height (sin) of a triangle which as a hypotenuse of length 1.    

Now, let's pick some examples. If we happen to set theta to 45 degress, you will get a triangle that looks like this:

In this case, both sin(theta) and cos(theta) are the same number, the square root of 1/2. So cos(theta) + cos (theta) is 2 times the square tool of 1/2.

Now imagine that we now want to find cos (theta + theta). Remember that theta was 45 degrees, so this will be cos (45 + 45), or cos (90).

But remember that cos is the base of a triangle where theta is the angle with the base. Well, that's not a triangle at all, is it? It's just a vertical line. In fact, cos(90) will be zero.

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation:

a

step-by-step explanation: