Asked by Matt
Can someone please explain (cos(x)+sin(x))/(cos(x)-sin(x)=sec(2x)+tan(2x). I have no luck with this. Thanks
Answers
Answered by
Reiny
RS
= 1/cos2x + sin2x/cos2x
= 1/(cos^2x - sin^2x) + 2sinxcosx/cos^2x - sin^2x)
= (1 + 2sinxcosx)/[(cosx+sinx)(cosx-sinx)]
= (sin^2x + 2sinxcosx + cos^2x)/[(cosx+sinx)(cosx-sinx)]
= (sinx + cosx)^2/[(cosx+sinx)(cosx-sinx)]
= (sinx + cosx)/(cosx - sinx)
= LS
= 1/cos2x + sin2x/cos2x
= 1/(cos^2x - sin^2x) + 2sinxcosx/cos^2x - sin^2x)
= (1 + 2sinxcosx)/[(cosx+sinx)(cosx-sinx)]
= (sin^2x + 2sinxcosx + cos^2x)/[(cosx+sinx)(cosx-sinx)]
= (sinx + cosx)^2/[(cosx+sinx)(cosx-sinx)]
= (sinx + cosx)/(cosx - sinx)
= LS
Answered by
Matt
Thank you very much!
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