how do you do sinAcosA=cosA-cos^3A/sinA
divide each term by cosA
sinA = 1 - cos^2A/sinA
multiply each term by sinA
sin^2A = sinA - cos^2A
sin^2A = sinA - (1 - sin^2A)
1 = sinA
A = 90º or pi/2 radians
or in general:
A = k(90)º or k(pi/2) radians
A = pi/2 + 2 n pi radians. n is any integer, including zero
To solve the equation sin(A)cos(A) = [cos(A) - cos^3(A)]/sin(A), we can start by simplifying the expression on both sides.
First, let's simplify the right side of the equation:
cos(A) - cos^3(A) = cos(A) - cos(A) * cos^2(A)
= cos(A) - cos^3(A)
= cos(A) * (1 - cos^2(A))
= cos(A) * sin^2(A) (using the identity 1 - cos^2(A) = sin^2(A))
Now, let's substitute this simplification into the original equation:
sin(A)cos(A) = cos(A) * sin^2(A) / sin(A)
Next, cancel out the sin(A) term on both sides:
cos(A) = sin^2(A)
Finally, take the square root of both sides to solve for sin(A):
sin(A) = ± sqrt(cos(A))
So, the solution is sin(A) = ± sqrt(cos(A)).