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.
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