prove that 2tan^-1 1/3 +tan^-1 1/7 = π/4
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Answer:
2tan
−1
(
3
1
)+tan
−1
(
7
1
)
=tan
−1
⎝
⎜
⎜
⎜
⎜
⎛
1−(
3
1
)
2
2×
3
1
⎠
⎟
⎟
⎟
⎟
⎞
+tan
−1
(
7
1
)
=tan
−1
⎝
⎜
⎜
⎛
9
8
3
2
⎠
⎟
⎟
⎞
+tan
−1
(
7
1
)
=tan
−1
(
4
3
)+tan
−1
(
7
1
)
=tan
−1
⎝
⎜
⎜
⎛
1−
4
3
×
7
1
4
3
+
7
1
⎠
⎟
⎟
⎞
[∵
4
3
×
7
1
<1]
=tan
−1
⎝
⎜
⎜
⎛
28
28−3
28
21+4
⎠
⎟
⎟
⎞
=tan
−1
(1)
=
4
π
.
Hence, proved.
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