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UPSC 2013 CDS 2 Math Paper
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© examsnet.com
Question : 93
Total: 100
What is
(
sin
θ
+
cos
θ
)
(
tan
θ
+
cot
θ
)
sec
θ
+
csc
θ
equal to?
[2013 CDS-II]
1
2
sin θ
cos θ
Validate
Solution:
(
sin
θ
+
cos
θ
)
(
tan
θ
+
cot
θ
)
sec
θ
+
csc
θ
=
(
sin
θ
+
cos
θ
)
(
sin
θ
cos
θ
+
cos
θ
sin
θ
)
1
cos
θ
+
1
sin
θ
=
(
sin
θ
+
cos
θ
)
(
sin
2
θ
+
cos
2
θ
cos
θ
sin
θ
)
sin
θ
+
cos
θ
cos
θ
sin
θ
=1
(
∵
sin
2
θ
+
cos
2
θ
=
1
)
Trick :
Take
θ
=
45
°
. Then
(
sin
45
∘
+
cos
45
∘
)
(
tan
45
∘
+
cos
45
∘
)
sec
45
∘
+
csc
45
∘
=
(
1
√
2
+
1
√
2
)
(
1
+
1
)
√
2
+
√
2
=
4
√
2
⋅
2
√
2
=
1
© examsnet.com
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