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NDA Math Trigonometric Ratios of Angles and Equations
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© examsnet.com
Question : 52
Total: 100
sinA
+
2
sin
2
A
+
sin
3
A
is equal to which of the following?
1.
4
sin
2
A
cos
2
(
A
2
)
2.
2
sin
2
A
(
sin
A
2
+
cos
A
2
)
2
3.
8
sinA
cosA
cos
2
(
A
2
)
Select the correct answer using the code given below:
[NDA II 2016]
1 and 2 only
2 and 3 only
1 and 3 only
1,2 and 3
Validate
Solution:
Let
A
=
30
°
⇒
sinA
+
2
sin
2
A
+
sin
3
A
=
sin
30
∘
+
2
sin
60
∘
+
sin
90
∘
=
1
2
+
2
√
3
2
+
1
=
2
√
3
+
3
2
(
∵
2
cos
2
A
=
1
+
cos
2
A
)
Now,
4
sin
2
A
cos
2
(
A
2
)
=
2
sin
2
A
[
1
+
cosA
]
=
2
sin
60
∘
[
1
+
cos
30
∘
]
=
2
√
3
+
3
2
Also,
sin
2
A
=
2
sinA
cosA
&
sin
2
A
+
cos
2
A
=
1
2
sin
2
A
[
sin
A
2
+
cos
A
2
]
2
=
2
sin
2
A
[
sin
2
A
2
+
cos
2
A
2
+
2
sin
A
2
cos
A
2
]
=
2
sin
2
A
[
1
+
sinA
]
=
2
sin
60
∘
[
1
+
sin
30
∘
]
=
3
√
3
2
&
8
sinA
cosA
cos
2
(
A
2
)
=
4
sinA
cosA
[
1
+
cosA
]
=
4
sin
30
∘
cos
30
∘
[
1
+
cos
30
∘
]
=
2
√
3
+
3
2
© examsnet.com
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