- 18. Given that tan (A + B) = 1 and that tan (A - B)
tan A and tan B.
find without using tables the values of
[SC]
2-1
Answers
Answered by
1
Step-by-step explanation:
tan
a
=
−
2
,
1
2
;
&
tan
b
=
−
3
,
1
3
.
Explanation:
METHOD I
Let
tan
a
=
x
,
tan
b
=
y
.
Given that,
tan
(
a
+
b
)
=
1
⇒
tan
a
+
tan
b
1
−
tan
a
tan
b
=
1
⇒
x
+
y
=
1
−
x
y
...
(
1
)
Similarly,
tan
(
a
−
b
)
=
1
7
⇒
x
−
y
=
1
7
(
1
+
x
y
)
...
...
...
.
(
2
)
(
1
)
+
(
2
)
⇒
2
x
=
8
7
−
6
7
x
y
,
or,
x
=
4
7
−
3
7
x
y
,
i.e.,
x
(
1
+
3
7
y
)
=
4
7
,
giving,
x
=
4
7
+
3
y
.
We submit this
x
in
(
1
)
to see that.
4
7
+
3
y
+
y
+
(
4
7
+
3
y
)
y
=
1
,
or,
4
+
7
y
+
3
y
2
+
4
y
=
7
+
3
y
,
i.e.,
3
y
2
+
8
y
−
3
=
0
.
Hence,
y
=
tan
b
=
−
3
,
1
3
.
Using
x
=
4
7
+
3
y
,
we get,
x
=
tan
a
=
−
2
,
1
2
.
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