Answer:
sin²A - sin²A cos²A not =sin¹A"
We can simplify the left-hand side of the given equation using the identity:
sin²A - sin²A cos²A = sin²A (1 - cos²A)
Then, we can use the identity sin²A + cos²A = 1 to substitute for cos²A:
sin²A (1 - cos²A) = sin²A sin²A
Multiplying the terms on the right-hand side, we get:
sin²A sin²A = (sinA)³
Therefore, the simplified left-hand side is (sinA)³.
Since the left-hand side of the given equation simplifies to (sinA)³ and the right-hand side is sinA raised to the power of 1, the given equation is not true in general.
Therefore, the statement "sin²A - sin²A cos²A = sin¹A" is not correct.