How do I go about completing the identity?

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  • ?
    Lv 7
    3 weeks ago

    cos (x - 11π/6) = cos x cos 11π/6 + sin x sin 11π/6

    ........................= (cos x)(√3/2) + (sin x)(-1/2)

    ........................= 1/2 [ √3 cos x - sin x ]...............ANS

  • 3 weeks ago

    The simplest way is to use the cosine-of-a-difference identity:

    cos (A - B) = (cos A)(cos B) + (sin A)(sin B)

    With B = 11*pi/6,

        cos B = cos (2pi - B) = cos (pi/6) = sqrt(3)/2

        sin B = - sin (2pi - B) = - sin (pi/6) = -1/2

    So cos (x - 11pi/6) = (sqrt(3)/2) cos x - (1/2) sin x, after substituting and simplfying.

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