Question 230151
Your equation to solve is:


sin^4(x)-cos^4(x)/sin^2(x)=1-cot^2(x)


Multiply both sides of this equation by sin^2(x) to get:


sin^4(x)-cos^4(x) = (1-cot^2(x)) * sin^2(x)


Remove parentheses on the right side of your equation to get:


sin^4(x)-cos^4(x) = sin^2(x) - (cot^2(x)) * sin^2(x))


Since cot(x) = cos(x) / sin(x), and (cos(x)/sin(x))^2 = cos^2(x)/sin^2(x), your equation becomes:


sin^4(x)-cos^4(x) = sin^2(x) - (cos^2(x)/sin^2(x)) * sin^2(x))


Simplify the right side of your equation to get:


sin^4(x)-cos^4(x) = sin^2(x) - cos^2(x)


Since sin^4(x) - cos^4(x) = (sin^2(x) + cos^2(x)) * (sin^2(x) - cos^2(x)), your equation becomes:


(sin^2(x) + cos^2(x)) * (sin^2(x) - cos^2(x)) = sin^2(x) - (cos^2(x)


Since sin^2(x) + cos^2(x) = 1, your equation becomes: 


sin^2(x) - cos^2(x) = sin^2(x) - (cos^2(x)


Since this is what you wanted to prove, you're done.