a+b=π\4,then (1+tan a)(1+tan b)=?
Answers
Answered by
0
Answer:
2
Step-by-step explanation:
first expand RHS and then it is easy to see.
also note that if a=π/4 and B=0 then( 1+1)(1+0)=2
Answered by
0
Explanation:
Given that,
A
+
B
=
π
4
,
we have,
tan
(
A
+
B
)
=
tan
(
π
4
)
.
∴
tan
A
+
tan
B
1
−
tan
A
tan
B
=
1
.
∴
tan
A
+
tan
B
=
1
−
tan
A
tan
B
.
∴
tan
A
+
tan
B
+
tan
A
tan
B
=
1
.
Adding on both sides, we get,
1
+
tan
A
−−−−−−−−
+
tan
B
+
tan
A
tan
B
−−−−−−−−−−−−−−−−−
=
1
+
1
.
∴
1
(
1
+
tan
A
)
+
(
1
+
tan
A
)
tan
B
=
2
.
∴
(
1
+
tan
A
)
(
1
+
tan
B
)
=
2
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