Question

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Answer 1

sin (θ + ϕ) = 2 sin (θ - ϕ)

sin (θ + ϕ) / sin (θ - ϕ) = 2

• Applying componendo and dividendo, we get

» sin(θ+ϕ)+sin(θ−ϕ)/sin(θ+ϕ)−sin(θ−ϕ) = (2+1)/(2-1)

» [2sin(θ+ϕ+θ−ϕ)/2 cos(θ+ϕ−θ+ϕ)/2] / [2cos(θ+ϕ+θ−ϕ)/2 sin(θ+ϕ−θ+ϕ)/2] = (2+1)/(2-1)

» [sin(2θ)/2 cos(2ϕ)/2] / [cos(2θ)/2 sin(2ϕ)/2] = (2+1)/(2-1)

» [sinθ cosϕ] / [cosθ sinϕ] = 3

» tanθ/tanϕ = 3

» tanθ = 3tanϕ