Answer:
To prove that cosA/sinA -sinA/cosA=2cos^2A-1/sinA cosA, we can start by multiplying both sides of the equation by sinA cosA:
cosA/sinA -sinA/cosAsinA cosA = (2cos^2A-1)/sinA cosAsinA cosA
Now we can simplify the left side of the equation by using the identity sin^2A + cos^2A = 1:
cosAcosA -sinAsinA = (2cos^2A-1)cosAsinA
Now we can simplify the right side of the equation by using the identity cos^2A = 1 - sin^2A:
cosAcosA -sinAsinA = (2(1 - sin^2A)-1)cosAsinA
Finally, we can simplify the right side of the equation by using the identity sinAcosA = (sinAcosA)/(sinA*cosA):
cosAcosA -sinAsinA = (2(1 - sin^2A)-1)(sinAcosA)/(sinA*cosA)
Since both sides of the equation are equal, we can conclude that the statement is true.