State whether the following are true or false. Justify your answer.
(i) `sin (A+B)=sin A+sin B`.
(ii) The value of `sintheta` increases as `theta` increases.
(iii) The value of `costheta` increases as `theta` increases.
(iv) `sintheta=costheta` for all values of `theta`
(v) `cot A` is not defined for `A = 0^@`

Explanation

Let's analyze each statement one by one and determine whether they are true or false, providing justifications for each.

### (i) `sin(A + B) = sin A + sin B`
**Solution:**
To check if this statement is true, we can use specific angle values. Let's take \( A = 30^\circ \) and \( B = 60^\circ \).

1. Calculate \( A + B \):
\[
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