Respuesta :
Answer:
λ represents a very large positive value (approaching positive infinity), and μ represents a real number depending on the specific range of tan(θ) allowed.
Step-by-step explanation:
Recognize the pattern: The expression involves tangent functions and aims to find the maximum and minimum values. This suggests utilizing trigonometric identities and analyzing the behavior of tangent across different angles.
Simplify the expression: We can rewrite the expression using the identity 1 + tan^2(θ) = sec^2(θ). This gives:
(7 + 6 tan θ - tan^2(θ)) / (1 + tan^2(θ)) = (7 + 6 tan θ) / (sec^2(θ))
Analyze the behavior of secant: Since secant is the reciprocal of cosine, it approaches positive or negative infinity depending on the quadrant and approaches 1 when the angle is zero or a multiple of π.
Maximum and Minimum:
Maximum: When the angle approaches a multiple of (π/2) where cosine (and hence secant) is zero, the expression tends to positive or negative infinity depending on the signs of 7 and 6 tan(θ). Let's assume the angle leads to a positive infinity, resulting in a very large positive value for the expression (λ).
Minimum: When the angle approaches 0 or π where secant is 1, the expression simplifies to 7 + 6 tan(θ). This value can be positive or negative depending on the value of tan(θ) within the allowed range (θ ≠ (2n+1)π/2). We'll denote the minimum value as μ.
