Respuesta :
Answer:
cos²θ = 1/2
Step-by-step explanation:
1. Initially, we are provided with the expression (tanθ - cotθ)/(tanθ + cotθ) + 2cos²θ = 1.
2. We start by substituting the values of tanθ and cotθ in the expression, which results in (sinθ/cosθ - cosθ/sinθ)/(sinθ/cosθ + cosθ/sinθ) + 2cos²θ = 1.
3. Next, we simplify the expression inside the brackets by finding a common denominator to combine the fractions effectively.
4. Upon simplification, the expression transforms into ((sin²θ - cos²θ)/(sinθcosθ)) / ((sin²θ + cos²θ)/(sinθcosθ)) + 2cos²θ = 1.
5. By further simplifying and dividing the fractions, we eventually arrive at (1 - 1) + 2cos²θ = 1.
6. Simplifying this expression leads us to 0 + 2cos²θ = 1.
7. Finally, by simplifying 2cos²θ = 1, we reach the conclusion that cos²θ = 1/2, which holds true.
This step-by-step process shows how the given expression was evaluated and simplified to reach the solution cos²θ = 1/2.
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