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UPSC CDS 2 2020 Math Paper
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© examsnet.com
Question : 21
Total: 100
Consider the following statements :
1) The value of
cos
61
°
+
sin
29
°
cannot exceed 1
2) The value of tan
23
°
−
cot
67
°
is less than
0
.
Which of the above statements is\are correct?
1 only
2 only
Bothe 1 and 2
Neither 1 nor 2
Validate
Solution:
Consider statement (1)
cos
61
°
+
sin
29
°
=
cos
(
90
−
29
)
°
+
sin
29
°
=
2
sin
29
°
For,
sin
30
°
=
1
2
⇒
2
sin
30
°
=
1
We know that
⇒
sin
29
°
<
sin
30
°
⇒
2
sin
29
°
<
2
sin
30
°
⇒
2
sin
29
°
<
1
⇒
cos
61
°
+
sin
29
°
<
1
Hence, statement (1) is correct.
Consider statement (2)
tan
23
°
−
cot
67
°
=
tan
23
°
−
cot
(
90
−
23
)
°
=
tan
23
°
−
tan
23
°
=
0
Hence, statement (2) is not correct.
© examsnet.com
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