Answer:
Explanation:
We can simplify the expression on the left-hand side using trigonometric identities:
tan(-A) = -tan(A) (since tan(-θ) = -tan(θ))
sin(180°+A) = -sin(A) (since sin(180°+θ) = -sin(θ))
sec(270°-A) = -cos(A) (since sec(270°-θ) = -cos(θ))
cos²(90°+A) = sin²A (since cos²(90°+θ) = sin²θ)
Substituting these values, we get:
-x.sin(A).cos(A).tan(A) = x.sin(-A) - sin²A.sin(A)
-x.sin(A).cos(A).tan(A) = -x.sin(A) - sin³A
Now, we can simplify this equation by moving all the terms to one side:
-x.sin(A).cos(A).tan(A) + x.sin(A) + sin³A = 0
Factoring out sin(A), we get:
sin(A) (-x.cos(A).tan(A) + x + sin²A) = 0
Since sin(A) ≠ 0, we can divide both sides by sin(A):
-x.cos(A).tan(A) + x + sin²A = 0
Multiplying both sides by cos(A), we get:
-x.sin(A) + x.cos²(A) + sin²A.cos(A) = 0
Using the identity cos²(θ) + sin²(θ) = 1, we can write this as:
-x.sin(A) + x(1 - sin²A) + sin²A.cos(A) = 0
Simplifying and rearranging, we get:
x = sin(A)/(cos(A) - sin²(A))
Therefore, the value of x is given by the expression sin(A)/(cos(A) - sin²(A)).