λ= 2tan(15 ∘ )−tan(45 ∘ )
Solution
Sure, let's solve this step by step:
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First, we need to know the values of tan(15°) and tan(45°). The value of tan(45°) is 1. The value of tan(15°) can be calculated using the formula tan(45° - 30°) = 1 - √3 / 1 + √3 = 2 - √3.
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Now, substitute these values into the equation: λ = 2tan(15°) - tan(45°) = 2(2 - √3) - 1.
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Simplify the equation: λ = 4 - 2√3 - 1 = 3 - 2√3.
So, λ = 3 - 2√3.
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