solve the equation

Question

Sinx / (1-cosx) - 1/sinx = 1/tanx   to  0< x <180 and 0< x < 360 

Answer 1

Angel,

 

I'm local in Gilbert, so Hello.

 

The solution turns out to be an identity that is true for all angles x that do not make a denominator go to zero.

 

SIN x/(1-COS x) - 1/SIN x = 1/TAN x = COS x/ SIN x  ,  since TAN = SIN x / COS x

Multiply both sides of the equation by SIN x to clear it as a denominator

 

SIN²x / (1-COS x) - 1 = COS x  and move the 1 to the right side

SIN²x / (1-COS x) = (1 + COS x)  , now clear the remaining denominator by multiplying both sides

SIN²x = (1 - COS x) (1 + COS x) = (1 - COS²x),  now move the COS²x to left side

 

SIN² x + COS² x = 1

 

In this form , this is a familiar relationship between SIn² & COS², and is true for all angles x since there is no possibility of division by zero in this expression.