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.
−π/3
No citable source has been recorded for this record. Treat it as practice material, not as fact.
tan−1(√3) = π/3 and sec−1(−2) = 2π/3, so the value is π/3 − 2π/3 = −π/3.
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
Write the principal value branch of tan−1x and of cot−1x.
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