Your answer is correct.
cos θ - tan θ * cos θ = 0
cos θ - sin θ/cos θ * cos θ = 0
cos θ - sin θ = 0
cos θ = sin θ
sin θ = cos θ
In interval:
0 < θ < 2 π
sin θ = cos θ
for
θ = π / 4 and θ = 5 π / 4
By the way this is trigonometry, not algebra.
solve the equation cos theta - tan theta * cos theta = 0 for 0< theta < 2 pi
My answer is pi/4,5pi/4
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