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cos-x-2cos-y-3-sin-x-y-2-2-3-what-is-sin-x-2sin-y-




Question Number 80941 by jagoll last updated on 08/Feb/20
cos x−2cos y=−(√3)  sin (x−y)=((2(√2))/3)  what is sin x−2sin y ?
cosx2cosy=3sin(xy)=223whatissinx2siny?
Commented by john santu last updated on 08/Feb/20
let sin x−2sin y = t  squaring   cos^2 x−4cos xcos y+4cos ^2 y=3  sin^2 x−4sin xsin y+4sin^2 y =t^2   sum : 5 −4cos (x−y) =t^2 +3  2−t^2  = 4cos (x−y)  from sin (x−y)=((2(√2))/3) ⇒cos (x−y)=(1/3)  ∴ 2−t^2 =(4/3) ⇒2−3t^2 =0  t = ± ((√6)/3)
letsinx2siny=tsquaringcos2x4cosxcosy+4cos2y=3sin2x4sinxsiny+4sin2y=t2sum:54cos(xy)=t2+32t2=4cos(xy)fromsin(xy)=223cos(xy)=132t2=4323t2=0t=±63
Commented by jagoll last updated on 08/Feb/20
thank you
thankyou

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