Which of the following is equivalent to 1/(1-cos(x)) - 1/(1+cos(x))?

Question

Which of the following is equivalent to 1/(1-cos(x)) - 1/(1+cos(x))? 

Please show every step

Answer 1

The common denominator is (1-cosx)(1+cosx) = 1-cos²x

 

So, 1/(1-cosx) - 1/(1+cosx) = (1+cosx)/(1-cos²x) - (1-cosx)/(1-cos²x)

 

                                        = 2cosx/(1-cos²x)

 

                                        = 2cosx/sin²x = 2(cosx/sinx)(1/sinx)

 

                                                            = 2(cotx)(cscx) 

 

 

Answer 2

Multiply by (1-cosx)(1+cosx).

 

then the problem becomes

 

(1+cosx) - (1-cosx) = 2cosx