State whether the following are true or false. Justify you answer.

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.

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