# 4.     State whether the following are true or false. Justify your answer.             $(i) \sin (A + B) = \sin A + \sin B$              $(ii)$  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 $A=0^{o}$

M manish

(i) False,
Let A = B =$45^0$
Then, $\\\sin(45^0+45^0) = \sin 45^0+\sin 45^0\\ \sin 90^ = 1/\sqrt{2}+q/\sqrt{2}\\ 1 \neq \sqrt{2}$

(ii) True,
Take $\theta = 0^0,\ 30^0,\ 45^0$
whent
$\theta$ = 0 then zero(0),
$\theta$ = 30 then value of $\sin \theta$ is 1/2 = 0.5
$\theta$ = 45 then value of $\sin \theta$ is 0.707

(iii) False,
$\cos 0^0 = 1,\ \cos 30^0 = \sqrt{3}/2= 0.87,\ \cos 45^0 = 1\sqrt{2}= 0.707$

(iv) False,
Let $\theta$ = 0
$\\\sin 0^0 = \cos 0^0\\ 0 \neq 1$

(v) True,
$\cot 0^0 = \frac{\cos 0^0}{\sin 0^0}=\frac{1}{0}$  (not defined)

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