Question

Solve for y in the equation y = 1+cos(x)/1-cos(x):

Answer 1

To solve for y in the equation y = 1+cos(x)/1-cos(x), simplify the expression and use the value of x.

Step-by-step explanation:

To solve for y in the equation y = 1+cos(x)/1-cos(x), we can simplify the expression on the right side of the equation. We'll start by multiplying the numerator and denominator by the conjugate of the denominator, which is 1+cos(x):

y = (1+cos(x))(1+cos(x))/(1-cos(x))(1+cos(x))

Simplifying further, we get:

y = (1+2cos(x)+cos^2(x))/(1-cos^2(x))

Using the identity cos^2(x) = 1-sin^2(x), we can rewrite the equation as:

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

y = (2+2cos(x)-sin^2(x))/(sin^2(x))

Now, to solve for y, we need to know the value of x and use it in the equation.