Same chapter3 marksDifficulty: Medium
Evaluate tan−1(1) + cos−1(1/2) + sin−1(1/2).
Inverse Trigonometric Functions
3 marksDifficulty: Medium
Prove that sin−1x + cos−1x = π/2 for x in [−1, 1].
Original Khojo Papers practice question — not from a past board paper.
Answer
Let sin−1x = θ, so sin θ = x with θ in [−π/2, π/2]. Then cos(π/2 − θ) = sin θ = x, and π/2 − θ lies in [0, π], which is the principal branch of the inverse cosine, so cos−1x = π/2 − θ and the sum is π/2.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
The corresponding identities hold for the tangent and cotangent, and for the secant and cosecant.
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