Trig indentiy problem

Question

Prove: Sec(2θ)= cos θ/ cosθ+ sinθ

+ sinθ/cosθ-sinθ

Answer 1

sec 2x =1/(cos²x-sin²x)=1/[(cos x+sin x)(cos x-sin x)]=[A cos x/(cos x +sin x)]+[B sin x/(cos x-sin x)]

Now show that A=B=1! OOOPS! This doesn't do it!

Alternatively, simply add the fractions on the rhs over the common denominator cos²x-sin²x.