I Suppose anyone can be good at trigonometry, all it takes is a willing mind and a good teacher.
Answer:
28
Step-by-step explanation:
From the given information:
Let x be the number of trees.
F(x) = (50 +x) (20 - 3x)
F(x) = 1000 - 150x + 20x - 3x²)
F(x) = -3x² - 130x + 1000
Differentiating F(x) with respect to x;


F'(x) = -6x -130
Now; we set F'(x) to be equal to zero to determine the critical value;
-6x - 130 = 0
x = - 130/6
Differentiating F''(x) with respect to x


F''(x) = -6 (<0)
Thus; by the second derivative, the revenue function F(x) is maximum when x = -130/6
Therefore, the number of trees she should plant per acre to maximize her harvest is:
50 + x = 50 - 130/6
= 85/3
28
Therefore, the number of trees per acre to maximize the harvest is 28
From the double-angle identity,

we can rewritte our given equation as:

By factoring 2cosx on the left hand side, we have

This equation has 2 solutions when

From equation (A), we obtain

and from equation (B), we have

On the other hand, we can find one more solution from the original equation by substituting x=0, that is,

then, x=0 is another solution. In summary, we have obtained the following solutions:

However, the intersection of the last set is empty. So the unique solution is x=0 as we can corroborate on the following picture:
Therefore, the solution set is: {0}