# 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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