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Byju's Answer
Standard XII
Mathematics
Sign of Trigonometric Ratios in Different Quadrants
If x ∈π/2, π,...
Question
If
x
∈
(
π
2
,
π
)
,
then
√
1
−
sin
x
1
+
sin
x
is equal to
A
tan
x
+
sec
x
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B
tan
x
−
sec
x
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C
sec
x
−
tan
x
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D
−
sec
x
−
tan
x
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Solution
The correct option is
B
tan
x
−
sec
x
√
1
−
sin
x
1
+
sin
x
=
√
(
1
−
sin
x
)
2
1
−
sin
2
x
=
√
(
1
−
sin
x
)
2
cos
2
x
=
|
(
1
−
sin
x
)
|
|
cos
x
|
=
1
−
sin
x
|
cos
x
|
(
∵
1
−
sin
x
≥
0
)
When
x
∈
(
π
2
,
π
)
,
then
|
cos
x
|
=
−
cos
x
, so
√
1
−
sin
x
1
+
sin
x
=
tan
x
−
sec
x
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2
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=