Question

√(1-cos4x)=sin4x хелп срочно

Answer 1

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Answer 2

To prove that √(1-cos4x) = sin4x, we can use the identity:

sin^2(x) + cos^2(x) = 1

We can rewrite the left-hand side of the equation as follows:

√(1-cos4x) = √[1 - (1 - 2sin^2(2x))] (using the identity cos(2θ) = 1 - 2sin^2(θ))

Simplifying the expression inside the square root:

√(1-cos4x) = √[2sin^2(2x)]

Using the identity sin(2θ) = 2sin(θ)cos(θ):

√(1-cos4x) = 2|sin(2x)|

Finally, using the identity sin(2θ) = 2sin(θ)cos(θ) again:

√(1-cos4x) = 2|sin(2x)| = 2|2sin(x)cos(x)| = 4|sin(x)cos(x)| = 2sin(2x) = sin4x

Therefore, we have proved that √(1-cos4x) = sin4x.