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Byju's Answer
Standard XII
Mathematics
Properties Derived from Trigonometric Identities
Solve ∫0π /...
Question
Solve
∫
π
/
2
0
cos
x
−
sin
x
1
+
sin
x
cos
x
d
x
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Solution
Let
I
=
∫
π
/
2
0
cos
x
−
sin
x
1
+
sin
x
cos
x
d
x
Using
∫
b
a
f
(
x
)
d
x
=
∫
b
a
f
(
a
+
b
−
x
)
d
x
∴
I
=
∫
π
/
2
0
cos
(
π
2
−
x
)
−
sin
(
π
2
−
x
)
1
+
sin
(
π
2
−
x
)
cos
(
π
2
−
x
)
d
x
=
∫
π
/
2
0
sin
x
−
cos
x
1
+
sin
x
cos
x
d
x
=
−
1
∴
2
I
=
0
⇒
I
=
0
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