Simplify :1/1-cosx +1/1+cos x

Assuming : 1/(1-cosx) +1/(1+cos x)

= (1+cosx + 1-cosx)/((1-cosx)(1+cosx))
= 2/(1 - cos^2 x) <------ did you notice the difference of squares

using sin^2 x + cos^2 x = 1, I will let you take another step

To simplify the expression 1/(1-cos(x)) + 1/(1+cos(x)), we can start by finding a common denominator for the two fractions.

The common denominator would be (1-cos(x))(1+cos(x)).

Now, let's rewrite the expression with the common denominator:

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

Expanding the numerators:

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

Simplifying the numerator:

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

Therefore, the simplified form of the expression 1/(1-cos(x)) + 1/(1+cos(x)) is 2/((1-cos(x))(1+cos(x))).