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We will learn how to prove the property of the inverse trigonometric function arccot(x) + arccot(y) = arccot(xy−1y+x) (i.e., cot−1 x - cot−1 y = cot−1 (xy−1y+x)
Proof:
Let, cot−1 x = α and cot−1 y = β
From cot−1 x = α we get,
x = cot α
and from cot−1 y = β we get,
y = cot β
Now, cot (α + β) = (cotαcotβ−1cotβ+tanα)
cot (α + β) = xy−1y+x
⇒ α + β = cot−1 xy−1y+x
⇒ cot−1 x + cot−1 y = cot−1 xy−1y+x
Therefore, cot−1 x + cot−1 y = cot−1 xy−1y+x
● Inverse Trigonometric Functions
11 and 12 Grade Math
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