Show that :(1 - sin A + cos A)^2= 2 (1 - sin A) (1 + cos A)

1.	Show that :(1 - sin A + cos A)^2= 2 (1 - sin A) (1 + cos A)
Answer» $\underline {\large \pmb{\mathfrak{๑ \: Question:}}}$ SHOW that : $\rm{(1-sinA+cosA)^2=2(1-sinA)(1+cosA)}$ $\\$ $\large \underline {\pmb{\mathfrak{๑ \: Solution:}}}$ $\rm (1-sinA+cosA)^2=LHS$ $\rm 1+sin^2A+cos^2A-2sinA-2sinAcosA+2cosA$ $\rm 1+1-2sinA-2sinAcosA+2cosA$ $\rm 2+2cosA-2sinA-2sinAcosA$ $\rm 2(1+cosA)-2sinA(1+cosA)$ $\rm (1+cosA)(2-2sinA)$ $\rm 2(1+cosA)(1-sinA)=RHS$ $\underline {\pmb{\mathfrak{Hence,~proved!}}}$ $\\$ $\large \underline{\pmb{\mathfrak{๑~More~to~know:}}}$ $\rm cos^2\theta +sin^2\theta=1$ $\rm 1+tan^2\theta=sec^2\theta$ $\rm 1+cot^2\theta=cosec^2\theta$ $\rm cosec(x \pm 2\pi)=cosecx$ $\rm tan(x \pm \pi)=tanx$ $\rm sin(x \pm y)=sinx~cosy \pm cosx~siny$ $\\$ ________________________________ Swipe your screen from LEFT to right in order to VIEW the ANSWER completely!

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$\underline {\large \pmb{\mathfrak{๑ \: Question:}}}$