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📐 Mathematics  ·  Inverse Trigonometric Functions  ·  JEE

sin-1 x + cos-1 x =

Answer: pi/2.

  • A pi
  • B pi/2
  • C 0
  • D 2pi

Correct answer: B. pi/2

Explanation: This is a fundamental identity: sin-1 x + cos-1 x = pi/2 for all x in [-1,1].

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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