Find number of solutions of the equation sin -1 (|log₂₆(cos x) - 1|) + cos -1 (|3 log₂₆(cos x) - 7|) = π/2, if x ∈ [0, 4π].

Trigonometry & Inverse Trigonometry

Inverse Trigonometric Equations

Grade 11

Question:

Find number of solutions of the equation sin-1(|log₂₆(cos x) - 1|) + cos-1(|3 log₂₆(cos x) - 7|) = π/2, if x ∈ [0, 4π].

Key Concept: Use the identity sin⁻¹(a) + cos⁻¹(b) = π/2 when a² + b² = 1, and analyze the logarithmic constraints.

Answer: 4

Correct Answer: 4