Inverse Trigonometric FunctionHard
Question
If sin-1 
+ cos-1 
=
, for 0 <|x| < √2, then x equals
+ cos-1 =, for 0 <|x| < √2, then x equals Options
A.1 / 2
B.1
C.- 1 / 2
D.- 1
Solution
We know that, sin-1 (α) + cos-1(α) =
Therefore, α should be equal in both functions.
∴
⇒
⇒
⇒
⇒ 2x(2 + x2) = 2x2 (2 + x)
⇒ 4x + 2x3 = 4x2 + 2x3
⇒ x(4 + 2x2 - 4x - 2x2) = 0
⇒ Either x = 0 or 4 - 4x = 0
⇒ x = 0 or x =1
∵ 0 < |x| < √2
∴ x = 1
and x ≠ 0
Therefore, α should be equal in both functions.
∴
⇒
⇒
⇒
⇒ 2x(2 + x2) = 2x2 (2 + x)
⇒ 4x + 2x3 = 4x2 + 2x3
⇒ x(4 + 2x2 - 4x - 2x2) = 0
⇒ Either x = 0 or 4 - 4x = 0
⇒ x = 0 or x =1
∵ 0 < |x| < √2
∴ x = 1
and x ≠ 0
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