16cos2x−29−815sinx21−16sin2x+8cosx=2 The Pythagorean Identity
sin2x+cos2x=1
Then
16(cos2x−1)−13−815sinx5+16(1−sin2x)+8cosx=2
−16sin2x−815sinx−1316cos2x+8cosx+5=2
Let u=sinx,v=cosx. Then
{u2+v2=116v2+8v+5=−32u2−1615u−26
{u2+v2=1(16v2+8v+1)+2(16u2+815u+15)=0
{u2+v2=1(4v+1)2+2(4u+15)2=0 Then
⎩⎨⎧u2+v2=14v+1=04u+15=0 Check
−16sin2x−815sinx−13=0
−16u2−815u−13=0 u=−415:
−16(−415)2−815(−415)−13
=−15+30−13=2=0 Hence
cosx=−41
x=±(π−arccos(41))+2πn,n∈Z
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