Simplify : cot^(2)x / cscx - 1
Prove the identity: cos^(4)x - sin^(4)x = cos(2)x-sin^(2)x
Please Help i really need the answers and steps. I am a little confused. Thanks
2006-11-27 10:13:00 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
#1
cot²x
----------- =
cscx - 1
csx²x - 1
------------ =
cscx - 1
(cscx + 1)(cscx - 1)
-------------------------- =
cscx - 1
cscx + 1
-------------------------- -------------------------- --------------------------
#2
cos^(4)x - sin^(4)x = cos^(2)x - sin^(2)x
LHS = cos^(4)x - sin^(4)x
= (cos²x - sin²x)(cos²x + sin²x)
= (cos²x - sin²x)( 1 )
= cos²x - sin²x
= RHS ....... QED
2006-11-27 10:21:12 · answer #1 · answered by Wal C 6 · 0⤊ 0⤋
cos^(4)x - sin^(4)x = cos^(2)x-sin^(2)x
cos^4 (x) - sin^4 (x) = [cos^2(x) - sin^2(x)](cos^2(x) + cos^2 (x)]
= cos^2(x) - sin^2(x)
2006-11-27 18:28:58 · answer #2 · answered by James Chan 4 · 0⤊ 0⤋