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UPSC NDA II 2014 Mathematics Paper
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© examsnet.com
Question : 40
Total: 120
If sin A sin (60°- A) sin (60°+A) = k sin 3A then, what is k equal to ?
[NDA II 2014]
1/4
1/2
1
4
Validate
Solution:
sinA
sin
(
60
°
−
A
)
sin
(
60
°
+
A
)
=
k
sin
3
A
⇒
sinA
(
sin
60
cosA
−
cos
60
sinA
)
(
sin
60
cosA
+
cos
60
+
sinA
)
=
k
sin
3
A
⇒
sinA
(
√
3
2
cosA
−
1
2
sinA
)
(
√
3
2
cosA
+
1
2
sinA
)
=
k
sin
3
A
⇒
sinA
(
3
4
cos
2
A
−
1
4
sin
2
A
)
=
k
sin
3
A
⇒
sinA
(
3
4
(
1
−
s
i
n
2
A
)
−
1
4
sin
2
A
)
=
k
sin
3
A
⇒
sinA
(
3
4
−
sin
2
A
)
=
k
sin
3
A
⇒
3
sinA
−
4
sin
3
A
4
=
k
sin
3
A
⇒
1
4
sin
3
A
=
k
sin
3
A
⇒
k
=
1
4
© examsnet.com
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