Question :
(i) Sin (A + B) = sin A + sin B
(ii) The value of \(sin \theta\) increases as \(\theta\) increases.
(iii) The value of \(cos \theta\) increases as \(\theta\) increases.
(iv) \(sin \theta\) = \(cos \theta\) for all values of \(\theta\).
(v) Cot A is not defined for A = 0.
Solution :
(i) False. Because
when A = 60 and B = 30. Then,
sin (A + B) = sin (60 + 30) = sin 90 = 1
and, sin A + sin B = sin 60 + sin 30 = \(\sqrt{3} + 1\over 2\)
So, sin (A + B) \(\ne\) sin A + sin B
(ii) True.
(iii) False
(iv) False. Because it is true for only \(\theta\) = 45
(v) True. Because tan 0 = 0 and cot 0 = \(1\over tan 0\) = \(1\over 0\) i.e. not defined.
