Prove that (cosA+cosB)²+(sinA-sinB)²=4cos²(A/2+B/2)

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Prove that (cosA+cosB)²+(sinA-sinB)²=4cos²(A/2+B/2)

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Ella 3 weeks 2021-11-19T14:16:37+00:00 1 Answer 0 views 0

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    2021-11-19T14:17:54+00:00

    Prove (cosA+cosB)^2+(sinA-sinB)^2 = 4cos^2(A+B)/2

    (cosA+cosB)^2 + (sinA-sinB)^2

    => (cos^2A + cos^2B + 2cosAcosB) + (sin^2A + sin^2B – 2sinAsinB)

    => cos^2A + cos^2B + sin^2A + sin^2B + 2cosAcosB – 2sinAsinB

    => cos^2A + sin^2A + cos^2B + sin^2B + 2(cosA*cosB – sinA*sinB)

    => 1 + 1 + 2(cosA*cosB – sinA*sinB)

    => 2 + 2(cosA*cosB – sinA*sinB)

    => 2 (1 + (cosA*cosB + sinA*sinB))

    => 2 * (1 + cos(A-B))

    {Because: cosA*cosB – sinA*sinB = cos(A+B)}

    => 2 * 2cos^2 ((A+B)/2)

    => 4cos^2 (A+B)/2

    Hope it helps please mark me as brainliest

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