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If sinθ+2sinϕ+3sinΨ=0 and cosθ+2cosϕ+3cosΨ=0 ; then evaluate :
a) cos3θ+8cos3ϕ+27cos3Ψ
b) sin(ϕ+ψ)+2sin(Ψ+θ)+3sin(θ+ψ)
 one year ago
 one year ago
If sinθ+2sinϕ+3sinΨ=0 and cosθ+2cosϕ+3cosΨ=0 ; then evaluate : a) cos3θ+8cos3ϕ+27cos3Ψ b) sin(ϕ+ψ)+2sin(Ψ+θ)+3sin(θ+ψ)
 one year ago
 one year ago

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mathsloverBest ResponseYou've already chosen the best response.0
I did the first one ... here : http://openstudy.com/study#/updates/511c70c9e4b06821731b25bc but second one is hard for me... can any1 help me?
 one year ago

.Sam.Best ResponseYou've already chosen the best response.0
For 2nd one did you try to use the tirg identities? e.g. sin(A+B)=sinAcosB+cosAsinB
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
hmn... no but ok i will try it now..
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
But where and how to use that formula @.Sam.
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
OK leave it can any one prove that if : a + 2b + 3c = 0 then : \[\large{\frac{1}{2} + \frac{2}{b} + \frac{3}{c} = 0 }\]
 one year ago

.Sam.Best ResponseYou've already chosen the best response.0
For \[3 \sin (\theta +\psi )+2 \sin (\theta +\Psi )+\sin (\psi +\phi )\] You just use it for each term You'll get \[\small 3 \sin(\theta )\cos (\psi )+3\cos (\theta ) \sin (\psi )+2\sin (\theta ) \cos(\Psi )+2 \cos(\theta ) \sin(\Psi )+\cos(\psi ) \sin(\phi )+ \sin(\psi ) \cos (\phi )\] Then try to factor it and apply ( sinθ+2sinϕ+3sinΨ=0 and cosθ+2cosϕ+3cosΨ=0 )
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
But is that proving or just verifying ?
 one year ago

.Sam.Best ResponseYou've already chosen the best response.0
its actually simplifying, try to factor that then your factored equation can apply this ( sinθ+2sinϕ+3sinΨ=0 and cosθ+2cosϕ+3cosΨ=0 ), which makes the equation smaller by equating them to 0.
 one year ago
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