Question

Sinx • cosx=а)cos4xб)0,5sin2xв)sin90г)2

Answer 1

Sinx * Cosx= 0,5sin2x

Answer 2

To solve the equation Sin(x) • Cos(x), we can use trigonometric identities. Let's go through the options one by one:

а) cos(4x) Using the double-angle identity for cos(2x), we have: cos(4x) = 2 * cos^2(2x) - 1 Substitute cos(2x) = 2 * cos^2(x) - 1: cos(4x) = 2 * (2 * cos^2(x) - 1)^2 - 1

This expression is quite complex and doesn't match Sin(x) • Cos(x).

б) 0.5 * sin(2x) Using the double-angle identity for sin(2x), we have: sin(2x) = 2 * sin(x) * cos(x)

Now, substitute this into the expression: Sin(x) • Cos(x) = Sin(x) • (2 * sin(x) * cos(x)) = 2 * sin^2(x) * cos(x)

This expression is different from 0.5 * sin(2x).

в) sin(90) sin(90°) = 1

This doesn't match Sin(x) • Cos(x).

г) 2 Finally, let's check if Sin(x) • Cos(x) equals 2: Sin(x) • Cos(x) = 2 * sin(x) * cos(x)

If we take x = 45°, then sin(45°) = cos(45°) = sqrt(2) / 2: Sin(45°) • Cos(45°) = 2 * (sqrt(2)/2) * (sqrt(2)/2) = 2 * (1/2) = 1

So, Sin(x) • Cos(x) doesn't equal 2 either.

None of the options match the expression Sin(x) • Cos(x). It's possible there may be a mistake in the given options or the question itself. Double-check the equation and provided options to ensure accuracy.