Question

Solve for x the equation arcsin(x) = arccos(x).​

Answer 1

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Answer 2

Answer:

We will learn how to prove the property of the inverse trigonometric function arcsin(x) + arccos(x) =

π

2

.

Proof: Let, sin−1 x = θ

Therefore, x = sin θ

x = cos (

π

2

- θ), [Since, cos (

π

2

- θ) = sin θ]

⇒ cos−1 x =

π

2

- θ

⇒ cos−1 x=

π

2

- sin−1 x, [Since, θ = sin−1 x]

⇒ sin−1 x + cos−1 x =

π

2

Therefore, sin−1 x + cos−1 x =

π

2

.