2007-08-01 03:41:24 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
cos x / [ sin x / cos x ]
cos ² x / sin x
(1 - sin ² x) / sin x
(1 / sin x) - sin x
2007-08-04 22:42:16 · answer #1 · answered by Como 7 · 0⤊ 0⤋
Simplify into sine and cosine:
cos x / tan x = cos x / (sin x / cos x) = (cos x)^2 / sin x
By the identity (sin x)^2 + (cos x)^2 = 1, (cos x)^2 = 1 - (sin x)^2. So by substitution:
(cos x) ^2 / sin x = ( 1 - (sin x)^2 ) / sin x
You could simplify this into: 1 / sin x - sin x
2007-08-01 10:48:01 · answer #2 · answered by Blue Wizard 2 · 0⤊ 0⤋
cox x/ tan x = (cos x) (1/ tan x)
Since tan x = sin x / cos x, (1/tan x) = cos x / sin x
Substitute for (1/tan x) in the first equation to get
cos x (cos x / sin x) = cos^x / sin x = (1 - sin^2 x) / sin x
2007-08-01 10:47:46 · answer #3 · answered by Optimizer 3 · 0⤊ 0⤋
subsitutetan x = ((Sin x)/(cos x))
=> (cos x)/[(Sin x)/(cos x)]
=>Cos^2 x/(sin x)
identities
1 - Sin^2 x = Cos^2 x
i.e. (1 - Sin^2 x)/(sin x)
2007-08-01 10:50:54 · answer #4 · answered by herbman76 2 · 0⤊ 0⤋
tan(x) = sin(x) / cos(x)
cos(x)/tan(x) = cos^2(x)/sin(x)
and cos^2(x) = 1 - sin^2(x)
so you get (1 - sin^2(x))/sin(x) or 1/sin(x) - sin(x)
2007-08-01 10:48:58 · answer #5 · answered by Captain Mephisto 7 · 0⤊ 0⤋
1-sin2 x/ sin x
2007-08-01 10:48:39 · answer #6 · answered by furball 4 · 0⤊ 0⤋
ITS QUITE SIMPLE ONE-1-SIN SQ X/SINX
2007-08-01 10:59:46 · answer #7 · answered by anushka 1 · 0⤊ 0⤋