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.