Trig Help

Geno, I think your answer is as far as it goes         

but I suspect that the intended question was a different one.

there probably should be brackets somewhere.   

cos(2a) - 1/cos(a) + 1

cos²(a) - sin²(a) - 1/cos(a) + 1                        ( Use the identity:  cos(2a) = cos²(a) - sin²(a) )

[cos³(a) - cos(a)sin²(a) - 1 + cos(a)]/cos(a)       ( Write with the common denominator:  cos(a) )

[cos³(a) + cos(a) - cos(a)sin²(a) - 1]/cos(a)       ( Rearrange the terms )

[cos³(a) + cos(a)[1 - sin²(a)] - 1]/cos(a)            ( Factor out cos(a) )

[cos³(a) + cos(a)[cos²(a)] - 1]/cos(a)                ( Use the identity:  cos²(a) = 1 - sin²(a) )

[cos³(a) + cos³(a) - 1]/cos(a)                           ( Multiply)

[2cos³(a) - 1]/cos(a)                                                       

... and now I'm stuck! ...

the perfect answer is

cos(2a-1)-cos(a+1)=0