if cos x = -1/3 and π < x < 3π/2.find sin x/2,cos x/2,tanx/2.
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11th
Maths
Trigonometric Functions
Trigonometric Equations
If pi/2 < x < pi , then √(1...
MATHS
If
2
π
<x<π, then
1+sinx
1−sinx
+
1−sinx
1+sinx
is equal to
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ANSWER
Given
2
π
<x<π,
1+sinx
1−sinx
+
1−sinx
1+sinx
=
1+sinx
1−sinx
+
1−sinx
1+sinx
=
(
1+sinx
)(
1−sinx
)
(
1−sinx
)
2
+(
1+sinx
)
2
=
1−sin
2
x
1−sinx+1+sinx
=
cos
2
x
2
=
∣cosx∣
2
As x∈(
2
π
,π),∣cosx∣=−cosx
So
1+sinx
1−sinx
+
1−sinx
1+sinx
=
−cosx
2
=−2secx