Question

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)

Answer 1

I did the first one ... here : http://openstudy.com/study#/updates/511c70c9e4b06821731b25bc

but second one is hard for me... can any1 help me?

Answer 2

For 2nd one did you try to use the tirg identities? e.g. sin(A+B)=sinAcosB+cosAsinB

Answer 3

hmn... no but ok i will try it now..

Answer 4

But where and how to use that formula @.Sam.

Answer 5

OK leave it can any one prove that if : a + 2b + 3c = 0 then :

\[\large{\frac{1}{2} + \frac{2}{b} + \frac{3}{c} = 0 }\]

Answer 6

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 )

Answer 7

But is that proving or just verifying ?

Answer 8

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.