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=2b2−2−4cosθcosϕ
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(θ−ϕ) but that didn't seem to be of much use
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