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Trigonometric Ratios CBSE NCERT Solutions Chapter 8 Exercise 8.2 Question 4

Trigonometric Ratios CBSE NCERT Solutions Chapter 8 Exercise 8.2 Question 4


 

4.   State whether the following are true or false. Justify your answer.

 

(i)  sin (A+B) = sin A + sin B

 

It is False. 

Let A = 60^\circ and B =30^\circ

 

L.H.S = sin (A+B) = sin(60^\circ+30^\circ) = sin(90^\circ) = 1

R.H.S = sin A + sin B = sin 60^\circ + sin 30^\circ = \frac{\sqrt{3}}{2} + \frac{1}{2}=\frac{\sqrt{3}+1}{2}

 

L.H.S \ne R.H.S

Therefore, the given statement is False.


 

(ii)  The value of sin \theta increases as \theta increases.

 

True. 

You can check here values of six trigonometric ratios (sin, cos, tan, sec, cot and cosec) for 0, 30, 45, 60 and 90 degrees. You can also learn from this article about how to memorize all the values in an easy way.


 

(iii)  The value of cos \theta increases as \theta increases.

 

False.

You can check here values of six trigonometric ratios (sin, cos, tan, sec, cot and cosec) for 0, 30, 45, 60 and 90 degrees. You can also learn from this article about how to memorize all the values in an easy way.


 

(iv) sin \theta = cos \theta for all values of \theta.

 

False

Example, sin 30^\circ=\frac{1}{2} but cos 30^\circ=\frac{\sqrt{3}}{2}


 

(v) cot A is not defined for A = 0^\circ

 

True

cot 0^\circ= \frac{cos 0^\circ}{sin 0^\circ}           (1)

But, sin 0^\circ=0     (2)

 

Putting (2) in (1), we get

cot 0^\circ= \frac{cos 0^\circ}{0} which is not defined.


 


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