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Byju's Answer
Standard XI
Mathematics
Theorems for Differentiability
If tan A-B=1 ...
Question
If tan (A − B) = 1 and sec (A + B) =
2
3
, the smallest positive value of B is
(a)
25
π
24
(b)
19
π
24
(c)
13
π
24
(d)
11
π
24
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Solution
(b)
19
π
24
Given
:
tan
(
A
-
B
)
=
1
and
sec
(
A
+
B
)
=
2
3
⇒
A
-
B
=
π
4
.
.
.
(
1
)
and
A
+
B
=
π
6
.
.
.
(
2
)
Adding
these
equations
we
get
:
2
A
=
π
4
+
π
6
⇒
A
=
5
π
24
⇒
Smallest
possible
value
of
B
=
π
-
5
π
24
=
19
π
24
.
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