I have the question "The instantaneous values of two alternating voltages are given by v1 = 5sinwt and v2 = 8sin(wt - pi/6). Using calculation obtain expressions for (a) v1 + v2 and (b) v1 - v2"
So for part (a) I used the cosine rule to get the maximum voltage which is 12.58 and then used the sine rule to find the phase angle and then derived an expression from these two.
However for part (b) I tried using the cosine rule to find the maximum voltage but because it is now subtracting rather than adding I changed the cosine rule so that it is 5$^2$-8$^2$ as opposed to 5$^2$+8$^2$.
The answer is get for the max voltage here is 5.5, how ever the solutions say that it should be 4.44.
Here is my attempt:
Where have I gone wrong ?
You simply wrote a wrong formula.
You can see the difference as:
$$V_1 - V_2 = V_1 + (- V_2)$$ and then do the maths.
Here is the correct one:
$$V_1 - V_2 = V_R = \sqrt{V_1^2 + V_2^2 + 2V_1 V_2 cos(150)}$$
That is
$$V_R = \sqrt{5^2 + 8^2 + 2\cdot 5 \cdot 8\cdot \cos(150)} = \sqrt{19.717967} = 4.44049$$