Final answer:
The attempt to prove that 41 cos θ = 40 using the given equation (9 sin θ + 40 cos θ = 41) does not yield a straightforward solution and requires reevaluation of the original claim.
Step-by-step explanation:
Given that 9 sin θ + 40 cos θ = 41, the aim is to prove that 41 cos θ = 40. We can approach this by recognizing that the given equation resembles a pattern of a trigonometric identity known as the Pythagorean identity, sin²θ + cos²θ = 1. If we divide the entire equation by cos θ, we get 9 tan θ + 40 = 41/cos θ. We can rearrange this to say tan θ = 41/cos θ - 40/9. Given the properties of trigonometric functions, tan θ = sin θ/cos θ. However, this step does not seem to apply directly to proving 41 cos θ = 40. Since the proof should result from valid mathematical steps and not assumptions or errors, the original claim might need a reevaluation or additional information to be solved correctly.