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📐 Mathematics  ·  Inverse Trigonometric Functions  ·  JEE

For x in [−1, 1], sin(sin⁻¹ x) equals:

Answer: x.

  • A x
  • B 1/x
  • C −x
  • D

Correct answer: A. x

Explanation: Applying sine to arcsine returns the original value x.

y = sin⁻¹x: Principal Value Branchxyx=-1x=1y=-π/2y=π/2Domain restricted to [-1,1]; range restricted to [-π/2,π/2] - this restriction is what makes the inverse exist

The graph of sin⁻¹x is confined to a narrow domain [-1,1] (since sine itself only takes values in that range) and range [-π/2,π/2] (the principal value branch chosen to make sine one-one and invertible there).

Concept context

Restricting trig functions to make them invertible, the principal value branches of sin-inverse, cos-inverse, tan-inverse, and friends, and the key identities relating them.

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