Prove (sin x/1+cos x) + (1+cos x/sin x) = 2 csc x?

1 ⤊

Prove (sin x/1+cos x) + (1+cos x/sin x) = 2 csc x?

2007-09-01 20:12:31 · 2 answers · asked by zyntax24 1 in Science & Mathematics ➔ Mathematics

2 answers

sinx/(1 + cosx) + (1 + cosx)/sinx
= ((sinx)^2 + (1 + (cosx)^2)/((sinx)(1 + cos x))
= ((sinx)^2 + (cosx)^2 + 2cosx + 1)/((sinx)(1 + cos x))
= 2(cosx + 1)/((sinx)(1 + cosx))
= 2/sinx
= 2cscx

2007-09-01 20:22:48 · answer #1 · answered by Bananaman 5 · 0⤊ 0⤋

[ sin ² x + (1 + cos x)² ] / [(sin x) (1 + cos x) ]
[sin²x + 1 + 2 cos x + cos²x ] / [(sin x)(1 + cos x)]
2(1 + cos x) / [sin x (1 + cos x)]
2 / sin x
2 cosec x

2007-09-05 10:52:52 · answer #2 · answered by Como 7 · 1⤊ 0⤋