`a)2cos^2 x-1=0`
`<=>1+cos 2x-1=0`
`<=>cos 2x=0<=>2x=\pi/2+k\pi<=>x=\pi/4+k\pi/2` `(k in ZZ)`
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`b)-2tan 2x+3=0`
`<=>tan 2x=3/2`
<=>2x=arctan(3/2)+k\pi<=>x=1/2arcta(3/2)+k\pi/2` `(k in ZZ)`
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`c)\sqrt{3}cot(2x+\pi/4)-1=0`
`<=>cot(2x+\pi/4)=\sqrt{3}/3`
`<=>2x+\pi/4=\pi/3+k\pi`
`<=>x=\pi/24+k\pi/2` `(k in ZZ)`
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`d)1/2sin(x-\pi/3)-1/4=0`
`<=>sin(x-\pi/3)=1/2`
`<=>[(x-\pi/3=\pi/6+k2\pi),(x-\pi/3=[5\pi]/6+k2\pi):}`
`<=>[(x=\pi/2+k2\pi),(x=[7\pi]/6+k2\pi):}` `(k in ZZ)`
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`e)2cos^2 x-3cos x+1=0`
`<=>[(cos x=1),(cos x=1/2):}`
`<=>[(x=k2\pi),(x=+-\pi/3+k2\pi):}` `(k in ZZ)`