Verify the trigonometric identity

How do I verify this identity?

(sec x + csc x) / (sin x + cos x) = 2 / (sin 2x)

I have no idea what to do, please help!

Thanks

RHS simplifies to 2/(2*sin(x)*cos(x)) = csc(x)*sec(x)

LHS also simplifies to:

(1/cos x + 1/sin x)/(sin x + cos x) = (1/sin(x)*cos(x)) = csc(x)*sec(x)

( sec x + csc x)/( sin x + cos x)

= [ (1/ cos x) + (1/ sin x) ]/ (sin x + cos x)

= [ sin x + cos x] /sin x cos x (sin x + cos x)

= 1/ sin x cos x

= 1 / (1/2) sin(2x)

= 2 / sin(2x)

Rewrite them in terms of sin.