Is sin x cos x ever equal to 1? Provide a reason for you answer.

When x = 0° : sin x = 0, cos x = 1, therefore sin x * cos x = 0.

Also, when x = 90° : sin x = 1, cos x = 0, so sin x * cos x = 0.

For any value between 0° and 90°, the product of sin and cos is less than 1.

We can show it like this:

sin 2 x = 2 sin x cos x (trigonometric formula)

sin x cos x = 1

sin 2 x / 2 = 1 / * 2 (we will multiply both sides of an equation by 2)

sin 2 x = 2 This is impossible because the maximum value for sin of any angle is 1.

Answer: sin x cos x is never equal to 1.