SOLUTION: show that 1+cos(x)/sin(x)=sin(x)/1-cos(x)
Algebra.Com
Question 282124: show that 1+cos(x)/sin(x)=sin(x)/1-cos(x)
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
show that 1+cos(x)/sin(x)=sin(x)/1-cos(x)
Let's start with the rigth-hand side above:
sin(x)/(1-cos(x))
Multiply above numerator and denominator by 1+cos(x):
(sin(x)*(1+cos(x))/((1-cos(x))*(1+cos(x))
(sin(x)+sin(x)*cos(x))/(1^2 -cos(x)+cos(x)-cos(x)^2)
(sin(x)+sin(x)*cos(x))/(1-cos(x)^2)
Using the identity sin(x)^2 + cos(x)^2 = 1 we know sin(x)^2 = 1 - cos(x)^2. So the above becomes:
(sin(x)+sin(x)*cos(x))/(sin(x)^2 =
(sin(x)/sin(x)^2) + (sin(x)*cos(x)/sin(x)^2) =
1/sin(x) + cos(x)/sin(x) =
(1 + cos(x))/sin(x)
RELATED QUESTIONS
Show that cos x / 1 + sin x + cos x / 1 - sin x = 2 sec... (answered by ikleyn)
{{{sin(x)/(1+cos(x))=(1-cos(x))/sin(x)}}} (answered by pmatei)
Show that: sin x cos^2x - sin x =... (answered by MathLover1)
Sin x + cos x = sin x / 1 - cos x / sin x + cos x / 1 - sin x / cos x
Verify that the... (answered by Alan3354)
sin^2x ? 1-cos... (answered by Alan3354)
sin x = cos 2x -... (answered by jsmallt9)
sin(2x)+cos(x)=1
(answered by AnlytcPhil)
show that cos (2arc sin... (answered by tommyt3rd)
verify that (sin x + cos x)^2 + (sin x - cos x)^2 =... (answered by Alan3354)