Simplify the expresssion: 1/(1+cosx) + 1/(1-cosx).

I have this urge to multiply.. but I think I should just make the denominators the same right? And then go from there?
=O

take the LCM & solve

[(1-cos x) + (1+cos x) ] / [(1+cos x)( (1-cos x)]


2 / (1-cos^2 x)

2 / sin^2 x

2 cosec^2 x

Common denominator = (1 + cosx)(1 - cosx)

1/(1+ cosx) + 1/(1 - cosx) = (1 - cosx + 1 + cosx)/(1 + cosx)(1 - cosx)
. . . . . . . . . . . . . . . . . . . = 2/(1 + cosx)(1 - cosx)
. . . . . . . . . . . . . . . . . . . = 2/(1 - cos²x)
. . . . . . . . . . . . . . . . . . . = 2/sin²x
. . . . . . . . . . . . . . . . . . . = 2 csc²x

Yes, use common denominator:

1/(1+cosx) + 1/(1-cosx)

= ((1-cosx) + (1+cosx)) / ((1+cosx)(1-cosx))

= 2 / (1-cos²x)

= 2 / sin²x

= 2 csc²x

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

2 Csc[x]^2