Verify:
cos^2x-cos^2xsin^2x=cos^4x
Somebody please help me... Thanks :)
^2 = squared
2007-05-17 17:47:25 · 3 answers · asked by countingmillions 1 in Science & Mathematics ➔ Mathematics
Factor out one of the cos^
cos^2 x * (1 - sin^2 x)
= cos^2 x * cos^2 x
= cos^4 x
2007-05-17 17:52:02 · answer #1 · answered by Dr D 7 · 1⤊ 0⤋
rearranging the left hand side...
cos^2(x) (1 - sin^2(x) )
now we know sin^2 (x) + cos^2 (x) = 1 therefore 1 - sin^2 (x) = cos^2 (x)
replacing into the rearranged left hand side...
cos^2 (x) cos^2 (x)
simplifying
cos^4 (x)
which is what you wanted to verify!!
2007-05-18 00:56:00 · answer #2 · answered by theanswerman 3 · 0⤊ 0⤋
LHS
= cos²x - cos²x.(1 - cos²x)
= cos²x - cos²x + cos^(4) x
= cos^(4) x = RHS
2007-05-18 09:22:17 · answer #3 · answered by Como 7 · 0⤊ 0⤋