2007-12-20 04:02:29 · 4 answers · asked by Yang W 1 in Science & Mathematics ➔ Mathematics
Left side:
(1 + 1/sin x) / (1 / cos x)
=[(sinx + 1) / sinx] * (cosx / 1)
=(sinxcosx + cosx) / sinx
Right side:
cosx + (cosx / sinx)
=(sinxcosx + cosx) / sinx
LS=RS, therefore the identity is true.
2007-12-20 04:06:33 · answer #1 · answered by Jacob A 5 · 0⤊ 0⤋
First, consider the following identities:
1 / cos x = sec x ; 1 / sec x = cos x
cos x / sin x = cot x
(1 + csc x) / sec x = 1 / sec x + csc x / sec x
= cos x + csc x / sec x
csc x = 1 / sin x
csc x / sec x = (1/sinx)/(1/cosx)
= cosx / sinx
So:
= cosx + cosx/sinx
= cosx + cotx
2007-12-20 12:07:18 · answer #2 · answered by Luke C 3 · 1⤊ 0⤋
LHS
(1+csc x)/sec x = 1/sec x + csc x/secx
=cos x + (1/sin)/(1/cosx) {1/sec = cos)
= cos x+ cosx/sinx
=cos x + cot x
Hence proved
2007-12-20 12:16:55 · answer #3 · answered by Sunny v 2 · 1⤊ 0⤋
Just observe that
(1+csc x)/sec x = (1+1/(sin x)) cos(x) = cos(x) + cos(x)/sin(x) = cot x, as stated.
2007-12-20 12:14:51 · answer #4 · answered by Steiner 7 · 0⤊ 0⤋