Question

Solve for:
1+cosx/sinx + sinx/1+cosx = 1

My teacher said no solution, but I don't know how he got that.

Answer 1

(1+cosx)/sinx + sinx/(1+cosx)
=
(1+cosx)^2 + sin^2x
------------------------
sinx(1+cosx)

1+2cosx+cos^2x+sin^2x
-------------------------
sinx(1+cosx)

= (2+2cosx)/(sinx(1+cosx))
= 2/sinx

so, does

2/sinx = 1

have any solutions?

Answer 2

cos x/sin x + sin x/(1+cos x) = 0 ??

nah, maybe you mean

(1+cos x)/sin x + sin x/(1+cos x)=1

(1+cos)(1-cos)/(sin(1-cos))
+sin (1-cos)/[(1+cos)(1-cos)] = 1

(1-cos^2)/(sin-sin cos)
+ (sin-sin cos)/(1-cos^2) = 1

sin/(1-cos) + (1-cos)/sin = 1

sin^2 + (1-cos)^2 = sin(1-cos)

(1-cos^2) +1 - 2 cos + cos^2 = sin-sin cos

2 - 2 cos = sin (1-cos)
humm
2 ( 1-cos) = sin(1-cos)

sin x = 2 !!!!!
well
-1 </= sin x </= +1
so impossible

Answer 3

Do I get extra credit for finding a harder way ?