Question

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

Answer 1

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.