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Online N
Lv 5
Online N asked in Science & MathematicsMathematics · 7 years ago

prove if sin x = n sin (x+2a) then prove that tan(x+a) = tan a (1+n)/(1-n)?

Update:

Prove if sin x = n sin (x+2a) then prove that tan(x+a) = (tan a) (1+n)/(1-n)?

1 Answer

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  • kiko
    Lv 5
    7 years ago

    sin x/ sin (x+2a= n/1

    By componendo and dividendo,

    (sin x +sin (x+2a))/ (sin x-sin (x+2a)) = (n+1)/(n-1)

    2 sin ((x+x+2a)/2) cos ((x-x-2a)/2)/ 2 cos ((x+x+2a)/2) sin ((x-x-2a)/2 =(n+1)/(n-1)

    Sin(x+a) cos(-a) /cos(x+a) sin(-a) =(n+1)/(n-1)

    Sin(x+a) cos a /(-cos(x+a) sin(a)) =(n+1)/(n-1)

    tan(x+a) = (tan a) (1+n)/(1-n)

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