Precalculus
posted by Joseph on .
Doing some test corrections and not seeing this....Please help:
Verify.
csc^4x  cot^4x = 2csc^2x1

Not a surprise that you don't get it,
the two expressions are not equivalent!
Start from left:
csc^4(x)cot^4(x)
Factor sin^4(x) as denominator:
=(1cos^4(x))/sin^4(x)
Factor as difference of two squares
= (1 + cos²(x)) (1  cos²(x)) / sin^4(x)
=(1 + cos²(x))sin²(x)/sin^4(x)
=(1+cos²(x))/sin²(x)
=(2cos²(x)+sin²(x))/sin²(x)
=2cos²(x)/sin²(x)+1
=2cot²(x)+1
(and not 2csc²(x)+1)