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Byju's Answer
Standard XII
Mathematics
Integration Using Substitution
If tan x 2=1-...
Question
If
tan
x
2
=
1
-
e
1
+
e
tan
α
2
, then
cos
α
=
(a)
1
-
e
cos
cos
x
+
e
(b)
1
+
e
cos
x
cos
x
-
e
(c)
1
-
e
cos
x
cos
x
-
e
(d)
cos
x
-
e
1
-
e
cos
x
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Solution
(d)
cos
x
-
e
1
-
e
cos
x
Given
:
tan
x
2
=
1
-
e
1
+
e
tan
α
2
⇒
tan
x
2
tan
α
2
=
1
-
e
1
+
e
Squaring
both
sides
,
we
get
,
tan
2
x
2
tan
2
α
2
=
1
-
e
1
+
e
⇒
tan
2
α
2
1
-
e
=
tan
2
x
2
1
+
e
⇒
sin
2
α
2
cos
2
α
2
1
-
e
=
sin
2
x
2
cos
2
x
2
1
+
e
⇒
1
2
1
-
cosα
1
2
1
+
cosα
1
-
e
=
1
2
1
-
cos
x
1
2
1
+
cos
x
1
+
e
⇒
1
-
cosα
1
+
cos
x
1
-
e
=
1
+
cosα
1
-
cos
x
1
+
e
⇒
1
+
cos
x
1
-
e
-
cosα
1
+
cos
x
1
-
e
=
1
-
cos
x
1
+
e
+
cosα
1
-
cos
x
1
+
e
⇒
cosα
1
+
cos
x
1
-
e
+
1
-
cos
x
1
+
e
=
1
+
cos
x
1
-
e
-
1
-
cos
x
1
+
e
⇒
cosα
=
2
cos
x
-
2
e
2
-
2
ecos
x
=
cos
x
-
e
1
-
ecos
x
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Q.
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