The number of solutions to cos(tan⁻¹(x)) = sin(cot⁻¹(3/4)) is:
The number of solutions to cos(tan⁻¹(x)) = sin(cot⁻¹(3/4)) is:
- A. 0
- B. 1
- C. 2
- D. 3
Answer: C) 2
Explanation: LHS: cos(tan⁻¹(x)) = 1 / √(1+x²). RHS: sin(cot⁻¹(3/4)). cot θ = 3/4 means opp=4, hyp=5, so sin θ = 4/5. 1 / √(1+x²) = 4/5 gives x² = 9/16, so x = ±3/4. Two solutions.
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