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📐 Mathematics  ·  Inverse Trigonometric Functions  ·  JEE

The value of arctan(1/2) + arctan(1/3) is:

Answer: π/4.

  • A π/6
  • B π/4
  • C π/3
  • D π/2

Correct answer: B. π/4

Explanation: Using the sum formula, ((1/2 + 1/3)/(1 − 1/6)) = 1, so the sum is arctan1 = π/4.

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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