Substitution method

Solve goniometric equation:


sin4 θ - 1/cos2 θ=cos2 θ - 2

Result

θ = (Correct answer is: k*pi) Wrong answer

Solution:

sin4θ1/cos2θ=cos2θ2 (1cos2θ)21/cos2θ=cos2θ2 t=cosθ  (1t2)21/t2=t22 t2 (1t2)21=t42t2 t62t4+t21=t42t2 t63t4+3t21=0 (t1)3(t+1)3=0  t1=1 t2=1  x1=arccos(t1)=arccos1=0 x2=arccos(t2)=arccos((1))3.1416 kZ  θ=x=k π



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