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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Multiples of an Angle
If α∈[π/2, π]...
Question
If
α
∈
[
π
2
,
π
]
,
then the value of
√
1
+
sin
α
−
√
1
−
sin
α
is
A
2
cos
α
2
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B
2
sin
α
2
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C
2
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D
2
tan
α
2
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Solution
The correct option is
A
2
cos
α
2
√
1
+
sin
α
−
√
1
−
sin
α
=
√
(
sin
α
2
+
cos
α
2
)
2
−
√
(
sin
α
2
−
cos
α
2
)
2
=
∣
∣
∣
sin
α
2
+
cos
α
2
∣
∣
∣
−
∣
∣
∣
sin
α
2
−
cos
α
2
∣
∣
∣
⋯
(
1
)
Now,
α
∈
[
π
2
,
π
]
⇒
α
2
∈
[
π
4
,
π
2
]
∴
sin
α
2
>
cos
α
2
⇒
sin
α
2
−
cos
α
2
>
0
⋯
(
2
)
From
(
1
)
and
(
2
)
,
√
1
+
sin
α
−
√
1
−
sin
α
=
sin
α
2
+
cos
α
2
−
sin
α
2
+
cos
α
2
=
2
cos
α
2
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0
Similar questions
Q.
If
α
∈
[
π
2
,
π
]
then the value of
√
1
+
sin
α
−
√
1
−
sin
α
is equal to:
Q.
If
α
ϵ
[
π
2
,
π
]
then the value of
√
1
+
s
i
n
α
−
√
1
−
s
i
n
α
is equal to
Q.
Given
π
2
<
α
<
π
, then the expression
√
1
−
sin
α
1
+
sin
α
+
√
1
+
sin
α
1
−
sin
α
=
Q.
If
sin
(
α
+
β
)
=
1
,
sin
(
α
−
β
)
=
1
2
,
α
,
β
∈
[
0
,
π
2
]
, then
Q.
If
sin
(
α
+
β
)
=
1
and
sin
(
α
−
β
)
=
1
/
2
where
α
,
β
ϵ
[
0
,
π
/
2
]
then
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