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maths (trigonometry)

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please solve these if possible

Q1. If sinx +siny=3(cosy-cosx) then the value of sin3x/sin3y.
Q2. If sina ,cosa,and tan a are in g.p.then cos cubea+cos square a is equal to

  • maths (trigonometry) -

    Q1.

    From the given relation, we can write, 3 cos x + sin x = 3 cos y - sin y

    put r cos ƒ¿=3 and r sin ƒ¿ = 1 , then we get , r = ã 10, tanƒ¿= 1/3

    so r cos ( x - ƒ¿) = r cos (x+ƒ¿)

    x = - y or x = }(y+ƒ¿)

    clearly x = - y satisfies the equation

    therefore, x = - y

    so 3x = -3y

    sin 3x = sin (-3y) = - sin 3y

    sin 3x / sin 3y = -1

  • maths (trigonometry) -

    ƒ¿= Greek letter Alpha

  • maths (trigonometry) -

    Q2)Because sina, cosa, tana - g.p.

    cos^2(a)=sina*tana=sin^2(a)/cosa
    cos^2(a)=(1-cos^2(a))/cosa

    cos^3(a)=1-cos^2(a)

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