# SOLUTION: How would you go about doing (1+cosx+sinx)/(1+cosx-sinx)=secx+tanx ?

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 Click here to see ALL problems on Proofs Question 373128: How would you go about doing (1+cosx+sinx)/(1+cosx-sinx)=secx+tanx ? Answer by CharlesG2(828)   (Show Source): You can put this solution on YOUR website!How would you go about doing (1+cosx+sinx)/(1+cosx-sinx)=secx+tanx ? sohcahtoa sin = opp/hyp, cos = adj/hyp, tan = opp/adj sin/cos = opp/hyp * hyp/adj = opp/adj tan = sin/cos sec = 1/cos sin^2(x)=(sinx)^2, cos^2(x) = (cosx)^2 trigonometric identity: (sinx)^2 + (cosx)^2 = 1 (1 + cosx + sinx)/(1 + cosx - sinx) = secx + tanx put all terms in terms of sin and cos: (1 + cosx + sinx)/(1 + cosx - sinx) = 1/cosx + sinx/cosx (1 + cosx + sinx)/(1 + cosx - sinx) = (1 + sinx)/cosx cross-multiply: cosx(1 + cosx + sinx) = (1 + sinx)(1 + cosx - sinx) distribute: cosx + (cosx)^2 + sinxcosx = 1 + cosx - sinx + sinx + sinxcosx - (sinx)^2 sinx terms on right cancel out cosx + (cosx)^2 + sinxcosx = 1 + cosx + sinxcosx - (sinx)^2 cosx terms and sinxcosx terms cancel out (cosx)^2 = 1 - (sinx)^2 (sinx)^2 + (cosx)^2 = 1, done