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UPSC CDS 1 2022 Math Paper
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© examsnet.com
Question : 5
Total: 100
What is the value of the following
2
sin
68
∘
cos
22
∘
−
2
cot
15
∘
5
tan
75
∘
−
3
tan
20
∘
tan
40
∘
tan
45
∘
tan
50
∘
tan
70
∘
5
−
1
0
1
5
Validate
Solution:
👈: Video Solution
Concept:
Using trigonometric ratios of complementary angles:-
-
sin
(
90
∘
−
θ
)
=
cos
θ
-
cos
(
90
∘
−
θ
)
=
sin
θ
-
tan
(
90
∘
−
θ
)
=
cot
θ
-
cot
(
90
∘
−
θ
)
=
tan
θ
-
cot
θ
=
1
tan
θ
Calculation:
2
sin
68
∘
cos
22
∘
−
2
cot
15
∘
5
tan
75
∘
−
3
tan
20
∘
tan
40
∘
tan
45
∘
tan
50
∘
tan
70
∘
5
⇒
2
sin
68
∘
cos
(
90
∘
−
68
∘
)
−
2
cot
15
∘
5
tan
(
90
∘
−
15
∘
)
−
3
tan
(
90
∘
−
70
∘
)
tan
(
90
∘
−
50
∘
)
tan
45
∘
tan
50
∘
tan
70
∘
5
⇒
2
sin
68
∘
sin
68
∘
−
2
cot
15
∘
5
cot
15
∘
−
3
tan
45
∘
cot
70
∘
cot
50
∘
tan
50
∘
tan
70
∘
5
⇒
2
sin
68
∘
sin
68
∘
−
2
cot
15
∘
5
cot
15
∘
−
3
tan
45
∘
⋅
1
tan
70
∘
⋅
1
tan
50
∘
⋅
tan
50
∘
⋅
tan
70
∘
5
⇒
2
sin
68
∘
sin
68
∘
−
2
cot
15
∘
5
cot
15
∘
−
3
tan
45
∘
5
⇒
2
−
2
5
−
3
×
1
5
[
∵
tan
45
∘
=
1
]
⇒
2
−
5
5
⇒
2
−
1
=
1
∴
The value of
2
sin
68
∘
cos
22
∘
−
2
cot
15
∘
5
tan
75
∘
−
3
tan
20
∘
tan
40
∘
tan
45
∘
tan
50
∘
tan
70
∘
5
is
1
.
© examsnet.com
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