Final answer:
To write the expression 1 - 2sin^2 25 as a single angle, we can use the double angle formula for sine and then simplify it using the product-to-sum formula.
Step-by-step explanation:
To write the expression 1 - 2sin^2 25 as a single angle, we can use the double angle formula for sine. The formula states that sin(2θ) = 2sin(θ)cos(θ). In this case, θ = 25 degrees. So we have:
1 - 2sin^2(25) = 1 - 2(2sin(25)cos(25)) = 1 - 4sin(25)cos(25).
This expression can be simplified further using another trigonometric identity. The product-to-sum formula states that 2sin(α)cos(β) = sin(α + β) + sin(α - β). Let α = β = 25 degrees:
1 - 4sin(25)cos(25) = 1 - 2[sin(50) + sin(0)] = 1 - 2sin(50).
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