sinx/1-cosx+1-cosx/sinx=2cscx

To simplify the left side of the equation, we need to find a common denominator.

sinx/1 - cosx can be multiplied by (1 + cosx) on both the numerator and denominator to get a common denominator of (1 - cos^2x) because of the identity sin^2x + cos^2x = 1.

So, sinx/1 - cosx becomes (sinx * (1 + cosx)) / (1 - cos^2x).

Now, let's simplify the right side of the equation.

2cscx can be rewritten as 2/sinx.

Now, we have:

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

Next, we need to simplify the expression further.

Since sin^2x = 1 - cos^2x, we can substitute it in the numerator.

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

The (1 - cos^2x) in the numerator and denominator cancels out.

1 + cosx = 2/sinx

Now, let's simplify the right side of the equation.

To get a common denominator, we multiply 2 by sinx/sinx.

2 * sinx/sinx = 2sinx/sinx

Now, the equation becomes:

1 + cosx = 2sinx/sinx

Cancel out sinx terms on both sides of the equation:

1 + cosx = 2

Now, subtract 1 from both sides to isolate cosx:

cosx = 1

So, the solution to the equation is cosx = 1.