Answer :
Given:
Here, we use some trigonometric formulas:
…(i) for |x| ≤ 1
…(ii) for y > 0
Now,
[from(i) & (ii)]
= tan [tan-1 x + tan-1 y]
We know that,
for xy < 1
OR
Taking LHS:
Now, we use the formula
for xy < 1
[in the first two terms, we applied the formula]
Now, we again apply the formula, we get
= tan-1(1)
= RHS
Hence Proved
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