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Grade: 11
        if cos alpha + cos two   alpha is equal to P and sin alpha + sin two alpha  is equal to Q then eliminate Alpha
one year ago

Answers : (1)

Kartik
26 Points
							For the sake of my convenience i am taking `alpha` as xNow we have,                    cosx +cos2x=P                    sinx+sin2x=Q            Squaring and adding the two         equations.    Then by rearranging we get    {(Sinx)^2+(cosx)^2}+{(sin2x)^2+(cos2x)^2}+2(sinx*sin2x+cosx*cos2x)=(P)^2+(Q)^2Now using the following trigonometric identities                 (Sink)^2+(cosk)^2=1.            (Identity 1)     Here k is any angle.                                Cos(A-B)=cosA*cosB+sinA*sinB.  (2nd idn)     Now going back to our question we get     1+1+2cosx=(P)^2+(Q)^2           From here we get            cosx=     {(P)^2+(Q)^2-2}/2       Now use it in the original equation to eliminate x.
						
one year ago
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