Math
posted by Matt on .
Can someone please explain (cos(x)+sin(x))/(cos(x)sin(x)=sec(2x)+tan(2x). I have no luck with this. Thanks

RS
= 1/cos2x + sin2x/cos2x
= 1/(cos^2x  sin^2x) + 2sinxcosx/cos^2x  sin^2x)
= (1 + 2sinxcosx)/[(cosx+sinx)(cosxsinx)]
= (sin^2x + 2sinxcosx + cos^2x)/[(cosx+sinx)(cosxsinx)]
= (sinx + cosx)^2/[(cosx+sinx)(cosxsinx)]
= (sinx + cosx)/(cosx  sinx)
= LS 
Thank you very much!