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.

### Statement (i): `sin(A + B) = sin A + sin B`
**Answer:** False
**Justification:** The correct formula for the sine of a sum is given by the identity:
\[ \sin(A + B) = \sin A \cos B + \cos A \sin B \]
Thus, the statement is false because it does not hold true for all values of A and B.

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