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  • State whether the following are true or false. Justify your answer. sin (A + B) = sin A + sin B

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}

Answers (1)

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(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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