Given:
To show: the above function is decreasing in R.
Explanation: Given
The first derivative is applied with respect to x,
By using the sum rule of differentiation, we get
Removing all the constant terms, we get
But the derivative of sin X = cos x and that of cos x = -sin x, so
Multiplying and dividing RHS by 2,
And we know, if , then f(x) is decreasing function.
Therefore, the given function is decreasing function in R.