Substitution method

Solve goniometric equation:


sin4 θ - 1/cos2 θ=cos2 θ - 2

Result

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

Solution:

sin⁡4θ−1/cos⁡2θ=cos⁡2θ−2 (1−cos⁡2θ)2−1/cos⁡2θ=cos⁡2θ−2 t=cos⁡θ  (1−t2)2−1/t2=t2−2 t2⋅ (1−t2)2−1=t4−2t2 t6−2t4+t2−1=t4−2t2 t6−3t4+3t2−1=0 (t−1)3(t+1)3=0  t1=1 t2=−1  x1=arccos⁡(t1)=arccos⁡1=0 x2=arccos⁡(t2)=arccos⁡((−1))≐3.1416 k∈Z  θ=x=k⋅ π

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