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UPSC NDA Math Model Paper 10
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© examsnet.com
Question : 54
Total: 120
What is the value of
sin
292
1
2
°
?
1
3
√
2
+
√
3
−
1
3
√
2
−
√
3
1
2
√
2
+
√
2
−
1
2
√
2
+
√
2
Validate
Solution:
Here,
sin
292
1
2
°
=
sin
(
585
2
)
°
We know,
cos
2
θ
=
1
−
2
sin
2
θ
⇒
√
1
−
cos
2
θ
2
=
sin
θ
∴
sin
(
585
2
)
°
=
√
1
−
cos
585
°
2
=
√
1
−
cos
(
360
+
225
)
2
=
√
1
−
cos
225
°
2
.
.
.
.
.
(
cos
(
360
+
θ
)
=
cos
θ
)
=
√
1
−
cos
(
180
+
45
)
°
2
=
√
1
+
cos
45
°
2
.
.
.
.
.
.
.
(
∵
cos
(
180
+
θ
)
=
−
cos
θ
)
=
√
1
+
1
√
2
2
.
.
.
.
.
.
(
cos
45
=
1
√
2
)
=
√
√
2
+
1
2
√
2
×
√
2
√
2
=
√
√
2
+
2
4
=
1
2
√
2
+
√
2
Hence, option (3) is correct.
© examsnet.com
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