Question

Sin4x–1/2=cos4x?????​

Answer 1

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Answer 2

To solve the equation sin(4x) - 1/2 = cos(4x), we can use trigonometric identities and algebraic techniques. First, let's manipulate the equation:

sin(4x) - 1/2 = cos(4x)

Now, we can use the Pythagorean identity for sine and cosine:

sin^2(4x) + cos^2(4x) = 1

Next, replace sin^2(4x) with 1 - cos^2(4x) in the equation:

(1 - cos^2(4x)) + cos^2(4x) - 1/2 = 0

Now, simplify the equation:

1 - cos^2(4x) + cos^2(4x) - 1/2 = 0

The cos^2(4x) terms cancel out:

1 - 1/2 = 0

Now, simplify further:

1/2 - 1/2 = 0

0 = 0

So, the equation sin(4x) - 1/2 = cos(4x) has no specific solutions for x. This means it is an identity, and it holds true for all real values of x.