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Byju's Answer
Standard IX
Mathematics
Complementary Ratios
Question 3 Wr...
Question
Question 3
Write ‘True’ or ‘False’ and justify your answer in each of the following:
The value of the expression,
(
s
i
n
80
∘
−
c
o
s
80
∘
)
is negative.
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Solution
The statement is false.
We know that,
s
i
n
θ
is increasing when
,
0
∘
≤
θ
≤
90
∘
and
c
o
s
θ
is decreasing when,
0
∘
≤
θ
≤
90
∘
∴
s
i
n
80
∘
−
c
o
s
80
∘
>
0
[positive]
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Q.
Question 2
Write ‘True’ or ‘False’ and justify your answer in each of the following:
The value of the expression
(
c
o
s
2
23
∘
−
s
i
n
2
67
∘
)
is positive.
Q.
Question 2
Write ‘True’ or ‘False’ and justify your answer in each of the following:
The value of the expression
(
c
o
s
2
23
∘
−
s
i
n
2
67
∘
)
is positive.
Q.
Write True' or False' and justify your answer in each of the following :
(i) The value of
sin
θ
is
x
+
1
x
, where 'x' is a positive real number .
(ii)
cos
θ
=
a
2
+
b
2
2
ab
, where a and b are two distinct numbers such that ab > 0.
(iii) The value of
cos
2
23
-
sin
2
67
is positive .
(iv) The value of the expression
sin
80
°
-
cos
80
°
is negative .
(v) The value of
sin
θ
+
cos
θ
is always greater than 1 .
Q.
Question 1
Write ‘True’ or ‘False’ and justify your answer in each of the following:
t
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47
∘
c
o
t
43
∘
=
1
Q.
Question 4
Write ‘True’ or ‘False’ and justify your answer in each of the following:
√
(
1
−
c
o
s
2
θ
)
s
e
c
2
θ
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