Double Angle Identity for Cosine I (sin & cos)
cosine2x=cos^2(x)-sin^2(x)
The double angle identity for cosine states that:
cos(2θ) = cos²(θ) – sin²(θ)
or
cos(2θ) = 2cos²(θ) – 1
We can derive this identity using the angle addition formula for cosine:
cos(α + β) = cos(α)cos(β) – sin(α)sin(β)
If we let α = β = θ, we get:
cos(2θ) = cos(θ + θ) = cos(θ)cos(θ) – sin(θ)sin(θ)
which simplifies to:
cos(2θ) = cos²(θ) – sin²(θ)
We can also use the Pythagorean identity (sin²(θ) + cos²(θ) = 1) to rewrite this as:
cos(2θ) = cos²(θ) – (1 – cos²(θ))
which simplifies to:
cos(2θ) = 2cos²(θ) – 1
More Answers:
The Essential Guide To Trigonometry: The Unit Circle And Its Role In Defining Standard Trigonometric Functions.Simplify Trigonometric Expressions With The Double Angle Identity For Cosine
Mastering The Double Angle Identity For Cosine And Its Sin Equivalent
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