Sunday, 27 January 2013

algebra precalculus - Find cos2theta+cos2phi, given sintheta+sinphi=a and costheta+cosphi=b


If

sinθ+sinϕ=aandcosθ+cosϕ=b



then find the value of cos2θ+cos2ϕ




My attempt:



Squaring both sides of the second given equation:



cos2θ+cos2ϕ+2cosθcosϕ=b2




Multiplying by 2 and subtracting 2 from both sides we obtain,



cos2θ+cos2ϕ=2b224cosθcosϕ



How do I continue from here?



PS: I also found the value of sin(θ+ϕ)=2aba2+b2



Edit: I had also tried to use cos2θ+cos2ϕ=cos(θ+ϕ)cos(θϕ) but that didn't seem to be of much use

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