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Byju's Answer
Standard XII
Mathematics
First Fundamental Theorem of Calculus
In any △ AB...
Question
In any
△
A
B
C
,
Π
(
sin
2
A
+
sin
A
+
1
sin
A
)
is always greater than :
A
9
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B
3
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C
27
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D
none of these
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Solution
The correct option is
D
27
Let
y
=
Π
(
sin
2
A
+
sin
A
+
1
sin
A
)
=
Π
[
1
+
(
sin
A
+
1
sin
A
)
]
Now we know in any triangle all
sin
A
,
sin
B
,
sin
C
are positive.
Thus using
A
.
M
≥
G
.
M
⇒
sin
A
+
1
sin
A
≥
2
Hence
y
≥
Π
(
1
+
2
)
=
27
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