maths

If cosA + sinA= root2 cosA
Show that cosA - sinA= root2 sinA

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  1. cosA + sinA= √2*cosA
    => sinA = √2*cosA - cosA
    => sinA = (√2 - 1)cosA

    cosA - sinA = cosA - (√2 - 1)cosA
    = √2*[cosA(√2 - 1)]
    = √2*sinA

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  2. cosA + sinA= √2*cosA
    (cosA + sinA)^2 = 2cos^2A
    cos^2A + 2sinAcosA + sin^2A = 2cos^2A
    cos^2A-sin^2A = 2sinAcosA
    (cosA+sinA)(cosA-sinA) = 2sinAcosA
    (√2*cosA)(cosA-sinA) = 2sinAcosA
    cosA-sinA = √2*sinA

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