SOLUTION: please help, prove: sin^4x-cos^4x/sin^2x=1-cot^2x

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Question 230151: please help, prove: sin^4x-cos^4x/sin^2x=1-cot^2x
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.