Evaluate tan−1(1) + cos−1(1/2) + sin−1(1/2).
Inverse Trigonometric Functions
Original Khojo Papers practice question — not from a past board paper.
The principal branch of tan−1x is (−π/2, π/2) and that of cot−1x is (0, π).
No citable source has been recorded for this record. Treat it as practice material, not as fact.
The end points are excluded because the tangent and cotangent are undefined there.
From the same topic and chapter, at a similar level.
Evaluate tan−1(1) + cos−1(1/2) + sin−1(1/2).
Inverse Trigonometric Functions
Evaluate tan−1(√3) − sec−1(−2).
Inverse Trigonometric Functions
Prove that sin−1x + cos−1x = π/2 for x in [−1, 1].
Inverse Trigonometric Functions
Find the principal value of sin−1(−1/2) and cos−1(−1/2).
Inverse Trigonometric Functions
If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], find AB and BA and state whether they are equal.
Matrices
Find the projection of a = 2i + 3j + 2k on b = i + 2j + k.
Vectors