and Cosine Subtraction Formulas
Now, we will try to prove the Sine and Cosine
Subtraction Formulas using the Figure 2 below.
a quadrilateral such that angle ABC and angle CDA are right angles
and angle DAB is acute. X denotes the angle DAB and Y denotes
the angle CAB. Thus angle CAD is X-Y.
Subtraction Formula states that
=sin(x)cos(y) - cos(x)sin(y).
see if we can prove this formula using the Figure 2 above!
we have proved the Sine Subtraction Formula does, in fact work
Now, let's try
proving the Cosine Subtraction Formula.
The Cosine Subtraction
=cos(x)cos(y) + sin(x)sin(y).
we have proved that the Cosine Subtraction Formula does work.