Substitution method

Solve a goniometric equation:


sin4 θ - 1/cos2 θ=cos2 θ - 2

Correct answer:

θ = k*pi

Step-by-step explanation:

sin4 θ  1/cos2 θ=cos2 θ  2 (1  cos2 θ)2  1/cos2 θ=cos2 θ  2 t = cos θ  (1t2)2  1/t2 = t2 2 t2   (1t2)2  1 = t4 2t2 t62t4+t2  1  = t4 2t2 t63t4+3t2  1  = 0 (t1)3(t+1)3 = 0  t1=1 t2=1  x1=arccos(t1)=arccos1=0 x2=arccos(t2)=arccos((1))3.1416 k  Z  θ=x=k π=k pi



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