Math

Prove the identities

1. cos3Ɵ + cos Ɵ = 4cos^Ɵ - 2 cos Ɵ
2. sin (A+B)sin (A-B)=cos2B + sin^2 A-1

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  1. hint for #1
    cos 3Ø = cos(2Ø + Ø)
    = cos2ØcosØ - sin2ØsinØ
    now replace cos2Ø = 2cos^-1 Ø - 1
    and sin2Ø = 2sinØcosØ
    very carefully expand and simplify

    2. Just as carefully replace sin(A+b)
    with sinAcosB + cosAsinB
    and sin(A-B) with sinAcosB - cosAsinB
    multiply them and see what comes out

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