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Step-by-step explanation:
Let, tan−1 x = α and tan−1 y = β
From tan−1 x = α we get,
x = tan α
and from tan−1 y = β we get,
y = tan β
Now, tan (α + β) = (tanα+tanβ1−tanαtanβ)
tan (α + β) = x+y1−xy
⇒ α + β = tan−1 (x+y1−xy)
⇒ tan−1 x + tan−1 y = tan−1 (x+y1−xy)
Therefore, tan−1 x + tan−1 y = tan−1 (x+y1−xy), if x > 0, y > 0 and xy < 1.
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Answers & Comments
✌
Step-by-step explanation:
Let, tan−1 x = α and tan−1 y = β
From tan−1 x = α we get,
x = tan α
and from tan−1 y = β we get,
y = tan β
Now, tan (α + β) = (tanα+tanβ1−tanαtanβ)
tan (α + β) = x+y1−xy
⇒ α + β = tan−1 (x+y1−xy)
⇒ tan−1 x + tan−1 y = tan−1 (x+y1−xy)
Therefore, tan−1 x + tan−1 y = tan−1 (x+y1−xy), if x > 0, y > 0 and xy < 1.