How do i verify:
cotx = (sin2x)/(1-cos2x)
http://www.jiskha.com/display.cgi?id=1195339028
To verify the given equation cot(x) = (sin(2x))/(1-cos(2x)), we can use trigonometric identities and algebraic manipulations.
Step 1: Rewrite sin(2x) and cos(2x) using double angle formulas:
sin(2x) = 2sin(x)cos(x)
cos(2x) = cos^2(x) - sin^2(x)
Step 2: Substitute the double angle formulas back into the equation:
cot(x) = (2sin(x)cos(x))/(1 - (cos^2(x) - sin^2(x)))
Step 3: Simplify the denominator:
cot(x) = (2sin(x)cos(x))/((1 - cos^2(x)) + sin^2(x))
= (2sin(x)cos(x))/(1 - cos^2(x) + sin^2(x))
= (2sin(x)cos(x))/(1 - (1 - sin^2(x)) + sin^2(x))
= (2sin(x)cos(x))/(1 - 1 + sin^2(x) + sin^2(x))
= (2sin(x)cos(x))/(2sin^2(x))
= cot(x)
Therefore, we have verified that cot(x) = (sin(2x))/(1-cos(2x)) holds true.