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
and B =30
L.H.S = sin (A+B) = sin(60
+30
) = sin(90
) = 1
R.H.S = sin A + sin B = sin 60
+ sin 30
=
L.H.S
R.H.S
Therefore, the given statement is False.
(ii) The value of sin
increases as
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
increases as
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
= cos
for all values of
.
False
Example, sin 30
but cos 30
(v) cot A is not defined for A = 0
True
cot 0
(1)
But, sin 0
(2)
Putting (2) in (1), we get
cot 0
which is not defined.
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